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?

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

How can you express √(a²b) in simplified form?

You can express √(a²b) as a√b, where a is the square root of the squared term, and b remains under the square root.

What is a quick way to approximate square roots of non-perfect squares?

To approximate square roots of non-perfect squares, find the closest perfect squares around the number. For example, √10 is between √9 (3) and √16 (4), so √10 is approximately 3.16.

Find the value of x: 2√x = 10.

Hint: Divide both sides by 2 first.

Divide both sides by 2: √x = 5. Square both sides: (√x)² = 5², which simplifies to x = 25.