What is a square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. for example, √9 = 3 because 3² = 9.

What is the rule for multiplying square roots?

To multiply square roots, multiply the values inside the square roots and then find the square root of the result. for example, √2 * √8 = √(2*8) = √16 = 4.

What is a tip for simplifying square roots?

To simplify square roots, find the prime factors of the number inside the square root and look for pairs of factors. for example, √18 = √(9*2) = 3√2.

Solve for x: √x = 5.

Hint: Square both sides to eliminate the square root.

Square both sides: (√x)² = 5², which simplifies to x = 25.

Solve the equation: √(x + 3) = 7.

Hint: Start by squaring both sides to remove the square root.

Square both sides: (√(x + 3))² = 7², which simplifies to x + 3 = 49. subtract 3 from both sides: x = 46.

What is the formula for the square of a binomial?

The square of a binomial (a + b)² is given by a² + 2ab + b². for example, (2 + 3)² = 2² + 2(2)(3) + 3² = 4 + 12 + 9 = 25.

How do you handle square roots of negative numbers?

The square root of a negative number is not defined in the set of real numbers. instead, it is represented using imaginary numbers: √(-a) = i√a.

If √x = √(2x - 8), what is x?

Hint: Square both sides and solve the resulting equation.

Square both sides: x = 2x - 8. rearranging gives x - 2x = -8, so -x = -8, thus x = 8.

For what value of x is √(x + 4) = 6?

Hint: Isolate the square root and square both sides.

Square both sides: (√(x + 4))² = 6², which simplifies to x + 4 = 36. subtract 4 from both sides: x = 32.