Question

Simplify each of the following:

a) root25 + root50 - root24 + root49

b) root2(2root8 – 3root32 + 4roor50)
Show your work

Answer 1

a.) 12 + 5√2 - 2√6

b.) 24

Explanation:

a) √25 + √50 - √24 + √49

• √25 + √50 - √24 + √49

Calculate the square root .

• 5 + √50 - √24 + 7

Simplify the radical expression.

• 5 + 5√2 - 2√6 + 7

Combine like terms.

• 5 + 7 + 5√2 - 2√6
• 12 + 5√2 - 2√6

b.) √2 ( 2√8 - 3√32 + 4√50 )

• √2 ( 2√8 - 3√32 + 4√50 )

Simplify the radical expression.

• √2 ( 4√2 - 3 × 2²√2 + 20√2)

Evaluate the power.

• √2 ( 4√2 - 3 × 4√2 + 20√2)

Calculate the products.

• √2 ( 4√2 -12√2 + 20√2)

Combine like terms.

• √2 × (4 - 12 + 20 )√2
• √2 × 12 √ 2

Multiply.

• 2 × 12
• 24

Answer 2

a)

• √25 + √50 - √24 + √49 =
• 5 + 5√2 - 2√6 + 7 =
• 12 + 5√2 - 2√6

b)

• √2(2√8 – 3√32 + 4√50) =
• 2√16 - 3√64 + 4√100 =
• 2*4 - 3*8 + 4*10 =
• 8 - 24 + 40 =
• 24