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 root of a product?

The formula states that √(a*b) = √a * √b. For example, √(4*9) = √4 * √9 = 2 * 3 = 6.

What is the formula for the square root of a quotient?

The formula states that √(a/b) = √a / √b. For example, √(16/4) = √16 / √4 = 4 / 2 = 2.

Simplify √(50). Hint: Factor 50 into its prime factors.

√(50) = √(25*2) = √25 * √2 = 5√2.

If √(x) = 12, what is x? Hint: Remember to square both sides.

Square both sides: (√x)² = 12², which simplifies to x = 144.

What is the value of √(x²) for any real number x?

The value of √(x²) is |x|, the absolute value of x, because the square root function returns non-negative values.