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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.

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Q: If you take the square root of an irrational number.Will it be irrational too?

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

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.

You get an irrational number as the square root.

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.

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.

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.

Any irrational number, and most rational 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

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

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

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.

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.

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.

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

you cant take the square root of a negative number

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.

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.

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.

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! âˆš42 is an irrational number between 5 and 7, its first 30 digits being 6.48074069840786023096596743608.

12i where i is the square root of -1

You can, if you consider complex numbers.

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

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.

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.

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