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 difference of squares?

The difference of squares states that a² - b² = (a - b)(a + b). For example, 9 - 4 = (3 - 2)(3 + 2) = 1 * 5 = 5.

If √x = 12, what is the value of x? Hint: Remember to square both sides.

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

What is the square root of a perfect square?

The square root of a perfect square is an integer. For example, √36 = 6 because 6² = 36.

How can you express √(a²) in simpler terms?

√(a²) = |a|, meaning the square root of a squared number is the absolute value of that number.

What is the square root of a fraction?

The square root of a fraction is found by taking the square root of the numerator and the denominator separately. For example, √(9/16) = √9 / √16 = 3/4.

If √x + 4 = 10, what is x? Hint: Isolate the square root first.

Isolate √x: √x = 10 - 4 = 6. Then square both sides: (√x)² = 6², which simplifies to x = 36.