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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.
