What is a surd?

A surd is an expression containing a square root, cube root, or other root that cannot be simplified to remove the root. For example, √2 and ∛5 are surds, while √4 = 2 is not, since it can be simplified.

How do you simplify the surd √(50)?

To simplify √(50), factor it into its prime factors: √(50) = √(25 * 2) = √25 * √2 = 5√2.

What is the rule for adding surds?

Surds can only be added if they are like terms, meaning they have the same radicand. For example, √2 + 3√2 = 4√2, but √2 + √3 cannot be simplified further.

Solve for x: √(x + 7) = 4.

Hint: Start by squaring both sides.

Square both sides: (√(x + 7))² = 4², which simplifies to x + 7 = 16. Subtract 7 from both sides: x = 9.

What is the product of the surds √3 and √12?

To find the product, multiply the values inside the square roots: √3 * √12 = √(3 * 12) = √36 = 6.

How do you rationalize the denominator of 1/√5?

To rationalize the denominator, multiply the numerator and denominator by √5: 1/√5 * √5/√5 = √5/5.

What is the value of √(18) + √(2)?

First, simplify √(18): √(18) = √(9 * 2) = 3√2. Thus, √(18) + √(2) = 3√2 + √2 = 4√2.

If a = √(12) and b = √(27), what is a + b?

Simplify first: a = 2√3, b = 3√3. Thus, a + b = 2√3 + 3√3 = 5√3.

Evaluate: √(x² + 6x + 9) for x = 2.

Hint: Recognize the expression as a perfect square.

The expression simplifies to √((x + 3)²). For x = 2, this becomes √((2 + 3)²) = √(5²) = 5.

What is the simplified form of √(8) - √(2)?

First simplify √(8): √(8) = 2√2. Thus, √(8) - √(2) = 2√2 - √2 = √2.

Calculate: (√7 + √3)(√7 - √3).

Use the difference of squares formula: (a + b)(a - b) = a² - b². Thus, = (√7)² - (√3)² = 7 - 3 = 4.

Is √(5) + √(5) equal to 2√(5)?

Yes, √(5) + √(5) = 2√(5) because they are like terms.