What is the definition of a square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √16 = 4 because 4 × 4 = 16.

How do you multiply square roots?

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

What is a rule for simplifying square roots?

To simplify square roots, factor the number inside the square root into its prime factors and remove pairs. For example, √50 = √(25 * 2) = 5√2.

Solve for x: √x = 7. Hint: Square both sides to eliminate the square root.

Square both sides: (√x)² = 7², which simplifies to x = 49.

Solve for x: √(x + 9) = 5. Hint: Start by squaring both sides to remove the square root.

Square both sides: (√(x + 9))² = 5², which simplifies to x + 9 = 25. Subtract 9 from both sides: x = 16.

What is the formula for the nth root of a number?

The nth root of a number a is expressed as a^(1/n). For example, the cube root of 8 is 8^(1/3) = 2.

How do you divide square roots?

To divide square roots, divide the values inside the square roots and then take the square root of the result. For example, √(9/4) = √9 / √4 = 3/2.

What is the cube root of 64?

The cube root of 64 is a number that, when multiplied by itself three times, equals 64. Thus, ∛64 = 4 since 4 × 4 × 4 = 64.

Simplify: √(x²y). Hint: Use the property of square roots to separate variables.

√(x²y) = √(x²) * √(y) = x√y.

What is the relationship between square roots and perfect squares?

A perfect square is an integer that is the square of an integer. For example, 1, 4, 9, and 16 are perfect squares because their square roots are integers.

If a² = 36, what is a? Hint: Consider both the positive and negative square roots.

A = ±√36, so a = ±6.

Find the value of x if ∛(x + 1) = 3. Hint: Begin by cubing both sides.

Cube both sides: (∛(x + 1))³ = 3³, which simplifies to x + 1 = 27. Thus, x = 26.

What is the simplified form of √(18)?

√(18) can be simplified to √(9 * 2) = 3√2.

If x = 25, what is √(x + 5)?

Substituting x into the expression, we get √(25 + 5) = √30.

How can you express the square root of a fraction?

The square root of a fraction a/b can be expressed as √a / √b. For example, √(1/4) = √1 / √4 = 1/2.