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 rule for adding square roots?

You can only add square roots directly if they have the same radicand. For example, √2 + √2 = 2√2, but √2 + √3 cannot be simplified further.

How do you simplify √(a²b)?

To simplify √(a²b), take the square root of the perfect square and leave the non-square part under the root: √(a²b) = a√b.

What is the square root of 0?

The square root of 0 is 0, since 0² = 0.

If x² = 36, what are the possible values of x? Hint: Consider both positive and negative roots.

The possible values of x are 6 and -6, since both (6)² and (-6)² equal 36.

What is the approximate value of √50? Hint: Find the closest perfect squares.

√50 can be simplified as √(25*2) = 5√2. The approximate value of √2 is about 1.414, so √50 ≈ 5 * 1.414 = 7.07.