answersLogoWhite

0


Best Answer

Certainly. Otherwise, there would be a rational number whose square was an irrational number; that is not possible.

To show this, let p/q be any rational number, where p and q are integers. Then, the square of p/q is (p^2)/(q^2). Since p^2 and q^2 must both be integers, their quotient is, by definition, a rational number. Thus, the square of every rational number is itself rational.

User Avatar

Wiki User

โˆ™ 2010-03-06 05:44:52
This answer is:
๐Ÿ™
0
๐Ÿคจ
0
๐Ÿ˜ฎ
0
User Avatar

Add your answer:

Earn +20 pts
Q: If you take the square root of an irrational number.Will it be irrational too?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

When you take the square root of an irrational number will the outcome be rational or irrational?

The square root of an irational number must, itself, be irrational.


Is root 2 a rational number?

The square root of 2 is irrational. In general, the square root of a positive integer is either an integer (if you take the square root of a perfect square), or it is irrational.


What happens when you take the square root of a non-perfect square?

You get an irrational number as the square root.


Are square root irrational?

Usually they are. More specifically, if you take the square root of a positive integer, there are only two possibilities:* If you take the square root of a perfect square, you get a whole number. * In all other cases, you get an irrational number.


Is the square root of .75 rational?

No. The square root of most numbers is irrational - only if the number of which you take the root happen to be perfect squares, do you get a rational root. In this case, to take the square root of 3/4, 3 is not a perfect square, so the root is not rational. Or you can take .75 to be 75/100; once again, 75 is not a perfect square, so the root is irrational.


Are square root numbers irrational?

Usually they are. More specifically, if you take the square root of a positive integer, there are only two possibilities:* If you take the square root of a perfect square, you get a whole number. * In all other cases, you get an irrational number.


What type of number can you take the square root of and it will be irrational?

Any irrational number, and most rational number.


Is the square root of negative 3 an irrational or a real number?

Neither. All irrational numbers are real numbers.Using the real number system you can't take the square root of a negative number, but if you're dealing with imaginary numbers then the square root of negative 3 is the square root of 3i


How do you solve x2 equals 10?

Take the square root of both sides. x=the square root of 10. It is an irrational number. Approximately 3.15


Is the square root of -25 irrational or complex?

you cant get the square root of a negative number. nothing times itself would equal a negative number. if you have √-25 then its not possible. If you have -√25 then you take the square root of 25 and make it negative, so then it would be -5


Irrational number between 8 and 9?

An irrational number is a number which cannot be expressed as a fraction made of integers. These numbers generally have infinite decimals with no pattern to them whatsoever. The easiest way, I think, to make an irrational number is to take the square root of a number between the squares of your parameters, in this case between 64 and 81. Thus a number such as square root(72), which is 8.485281..., or square root(80), which is 8.944571..., will do nicely.


How do you find an irrational number between two irrational numbers?

There may be many easier and better ways, but here's how I would do it: -- Square the first given irrational number. -- Square the second irrational number. -- Pick a nice ugly complicated decimal between the two squares. -- Take the square root of the number you picked. It's definitely between the two given numbers, and it would be a miracle if it's not irrational.


Are square roots real numbers?

Yes, if the number whose square root we are taking is greater than 0. Only if you try to take the square root of a negative number will you get back an imaginary number. Square roots are often irrational, but that's different from real versus imaginary.


What is the square root of the square root of 1?

The square root of 1 is also 1, so then you just take the square root of that, which is, again, 1.


Square root of -12 plus square root of 300?

you cant take the square root of a negative number


Irrational number between 50 and 70?

An irrational number is a number which cannot be expressed as a fraction made of integers. These numbers generally have infinite decimals with no pattern to them whatsoever. The easiest way, I think, to make an irrational number is to take the square root of a number between the squares of your parameters, in this case between 2500 and 4900. Thus a number such as square root(2738), which is 52.325901..., or square root(4677), which is 68.388595..., will do nicely. In this case make sure you check your answer because some numbers such as 3600 will lead to whole number (and non-irrational) answers.


How do you figure the square root of a house?

You don't take the square root of a house, or of any object for that matter. You can take a square root of numbers, and of certain measurements, for example, the house's surface area.You don't take the square root of a house, or of any object for that matter. You can take a square root of numbers, and of certain measurements, for example, the house's surface area.You don't take the square root of a house, or of any object for that matter. You can take a square root of numbers, and of certain measurements, for example, the house's surface area.You don't take the square root of a house, or of any object for that matter. You can take a square root of numbers, and of certain measurements, for example, the house's surface area.


Find the diagonal of a square whose are is 36?

First, take the square root, to get the length of a side. Then (because of Pythagoras), multiply the length of the side by the square root of 2.First, take the square root, to get the length of a side. Then (because of Pythagoras), multiply the length of the side by the square root of 2.First, take the square root, to get the length of a side. Then (because of Pythagoras), multiply the length of the side by the square root of 2.First, take the square root, to get the length of a side. Then (because of Pythagoras), multiply the length of the side by the square root of 2.


How do you find an irrational number between the twin primes 5 and 7?

Square them both, find a non-square integer between those two results, and then take the square root of that number. In other words, find a non-square integer between 25 and 49, and since there is only one square number between them, 36, that should be easy; let's pick 42, and then take the square root of it. Ta da! √42 is an irrational number between 5 and 7, its first 30 digits being 6.48074069840786023096596743608.


What is the square root of -144?

12i where i is the square root of -1


Can you take the square root of a negative number?

You can, if you consider complex numbers.


How do you find the length of the side of the square?

Measure it. Or take a quarter of its perimeter. Or take the square root of its area. Or take the cube root of a cube built on the square


What is the sqaure root of 72?

The square root of 72 is 6x(sqrt2). You can find this by breaking 72 down into its prime factors (2x6x6 or 2x62). You can then take the square root of each part which means the 62 will become 6 and then because the sqrt2 is an irrational number it is left under the sqrt sign.


What is the simplied eqation square root of 30 multiplied by the square root of 12?

Multiply the thirty and the twelve together to get three hundred and sixty. Now you have the square root of three hundred and sixty. Then take out any square roots you know. In 360, the obvious choice is 36. Take the square root of 36, six, out of the square root. When you take thirty-six out, you are left with the square root of ten. You now have six square root of ten.


What is the square root of space?

That makes no sense. You take the square root of numbers, and of certain measurements - not of "space".