Algebra: Manipulating Surds

The video tutorial covers three main algebraic concepts: simplifying surds, rationalizing denominators, and completing the square. In Part A, the focus is on expressing surds in terms of root 5. Part B involves rationalizing denominators and expressing results in the form of P plus root Q. Part C demonstrates completing the square to express quadratic equations in the form of X plus A squared plus B.

What is the simplified form of √45?

• 3√5

• 5√3

• √9 + √5

• 9√5

How do you express √20 in terms of √5?

• 5√2

• 4√5

• √4 + √5

• 2√5

What is the result of adding 3√5 and 2√5?

• 5√5

• 6√5

• √25

• 5√10

What is the first step in rationalizing the denominator of 2/(√3 - 1)?

• Multiply by 2

• Multiply by √3 - 1

• Multiply by √3 + 1

• Multiply by 1

After rationalizing the denominator, what is the simplified form of 2/(√3 - 1)?

• 1 - √3

• √3 - 1

• 2 + √3

• 1 + √3

In the expression 2/(√3 - 1), what is the purpose of multiplying by the conjugate?

• To change the sign of the numerator

• To add a surd to the numerator

• To simplify the numerator

• To eliminate the surd in the denominator

What is the first step in completing the square for X^2 + 6√2X - 1?

• Add 6√2

• Subtract 1

• Expand the expression

• Set up two brackets

What value is subtracted to complete the square in the expression X^2 + 6√2X - 1?

• 18

• 9

• 6√2

• 3√2

What is the final form of the expression X^2 + 6√2X - 1 after completing the square?

• (X + 3√2)^2 + 1

• (X + 3√2)^2 - 19

• (X + 3)^2 - 18

• (X + 6√2)^2 - 1

Why is it necessary to subtract 3√2 squared in the process of completing the square?

• To eliminate the surd

• To simplify the expression

• To balance the equation

• To add a constant