0
Add your answer:
Earn +20 pts
What are the positive and negative square roots of 1?
The numbers 1 and negative 1 (-1) are both square roots of positive 1.The square root of negative 1 is the "imaginary" number i.
How many square roots do negative numbers have?
Negative numbers do not have "real number" square roots.However, they will have two roots (when using imaginary numbers) as do other numbers, where a root including i(square root of -1) is positive or negative.
Why do square roots have two solutions and cube roots only have one solution?
Square roots only have two solutions if the number is positive, if the number is negative it has no solutions.Actually ALL numbers (including negative numbers) have two square roots and three cube roots - just not all of them are real numbers; some are complex numbers.What is a complex number?A complex number is a number which is the sum of two parts: a real part and an imaginary part, ie are of the form (a + bi):a is the real part;bi is the imaginary part which is a real number (b) multiplied by the square root of -1 which is an imaginary value. To avoid having to write √-1 all the time, the little 'i' is used instead, ie i² = -1.Now the square roots of negative numbers can be found:eg √-4 = √(4 × -1) = √4 √-1 = 2i → the square root of -4 is ±2i.What about cube roots?³√8 = 2 is the real root, but there are two further complex roots: (-1 + √3 i) and (-1 - √3 i). I'll cube the first to show it does indeed equal 8 (remember that i² = -1)(-1 + √3 i)³ = (-1 + √3 i)(-1 + √3 i)(-1 + √3 i)= (-1 + √3 i)((-1)×(-1) + -1 × √3 i + -1 × √3 i + (√3 i)×(√3 i))= (-1 + √3 i)(1 - 2 (√3 i) + 3i²)= (-1 + √3 i)(1 - 2 (√3 i) + 3 × -1)= (-1 + √3 i)(1 - 2 (√3 i) - 3)= (-1 + √3 i)(-2 - 2 (√3 i))= (-1 + √3 i)(-1 - √3 i) × 2= ((-1)² - (√3 i)²) × 2= (1 - (-3)) × 2= (1 + 3) × 2= 4 × 2= 8Similar cubing of (-1 - √3 i) equals 8.
What is the Square root of 160?
Negative numbers do not have square roots. Multiplying any number by itself will always be a positive number. For example, -1 x -1 is 1. Because two negatives cancel themselves out, and regular numbers are always positive.
When the square root of one number is subtracted from the square root of another the difference is 1 less than the square of 9?
Try the square roots of 1 and 6561, which are 1 and 81. Their difference is 80 which is one less than 81. And that is the square of 9. In fact this works whenevr the first of the two numbers is a square number. So the purpose of the question is not clear.
How do you found two squares roots for 1?
The two square roots are -1 and +1.For any real number, x, other than 0, if y is the square root of x then so is -y.
How do you find the two square roots of i imaginary number Answer in rectangular form?
The two square roots of i are (k, k) and (-k, -k) where k = sqrt(2)/2 = 1/sqrt(2).
What are two square roots for1?
-1 and +1.
What are the positive and negative square roots of 1?
The numbers 1 and negative 1 (-1) are both square roots of positive 1.The square root of negative 1 is the "imaginary" number i.
What is a square number between 1 and 4?
There is no perfect square number between 1 and 4. On the other hand, every number is a square - or its square roots.
How many square roots do negative numbers have?
Negative numbers do not have "real number" square roots.However, they will have two roots (when using imaginary numbers) as do other numbers, where a root including i(square root of -1) is positive or negative.
If you get a whole number while doing square roots what would the answer be rational or irrational?
A rational number is a number that can be expressed as the division of two integers, while the divisor is not zero. An irrational number is any number that is not rational.Whole numbers are rational, because the divisor is 1. It has nothing to do with square roots.
What is the fourth root of 1?
The two real roots are -1 and +1.There are also two roots in the complex field and these are ±i where i is the imaginary square root of -1.
Is the square root of a non perfect square an irrational number?
No.1/4 is not a perfect square but its square roots are +/- 1/2 which are rational.
What are two square roots of -36?
There are no real numbers, only in the imaginary field they are -6i and 6i where i is the imaginary square root of -1.
Is the square root of a natural number be negative?
"Natural number" means all of the ordinary counting numbers ... everywhole number starting with ' 1 ' and counting up.Every one of these natural numbers has two square roots ... one positiveand one negative. Both square roots have the same digits, and only theirsigns are different.
Why do square roots have two solutions and cube roots only have one solution?
Square roots only have two solutions if the number is positive, if the number is negative it has no solutions.Actually ALL numbers (including negative numbers) have two square roots and three cube roots - just not all of them are real numbers; some are complex numbers.What is a complex number?A complex number is a number which is the sum of two parts: a real part and an imaginary part, ie are of the form (a + bi):a is the real part;bi is the imaginary part which is a real number (b) multiplied by the square root of -1 which is an imaginary value. To avoid having to write √-1 all the time, the little 'i' is used instead, ie i² = -1.Now the square roots of negative numbers can be found:eg √-4 = √(4 × -1) = √4 √-1 = 2i → the square root of -4 is ±2i.What about cube roots?³√8 = 2 is the real root, but there are two further complex roots: (-1 + √3 i) and (-1 - √3 i). I'll cube the first to show it does indeed equal 8 (remember that i² = -1)(-1 + √3 i)³ = (-1 + √3 i)(-1 + √3 i)(-1 + √3 i)= (-1 + √3 i)((-1)×(-1) + -1 × √3 i + -1 × √3 i + (√3 i)×(√3 i))= (-1 + √3 i)(1 - 2 (√3 i) + 3i²)= (-1 + √3 i)(1 - 2 (√3 i) + 3 × -1)= (-1 + √3 i)(1 - 2 (√3 i) - 3)= (-1 + √3 i)(-2 - 2 (√3 i))= (-1 + √3 i)(-1 - √3 i) × 2= ((-1)² - (√3 i)²) × 2= (1 - (-3)) × 2= (1 + 3) × 2= 4 × 2= 8Similar cubing of (-1 - √3 i) equals 8.
