Simplify square root of 5 open parentheses 10 minus 4 square root of 2 close parentheses.

Solution:

It is given that square root of 5 open parentheses 10 minus 4 square root of 2 close parentheses

We can write it as √5(10 - 4√2)

Using the multiplicative distributive property

√5(10 - 4√2) = 10√5 - 4√2√5 = 10√5 - 4√10

Therefore, by simplifying we get (10√5 - 4√10).

Example - 

Simplify square root of 2 open parentheses 5 minus 3 square root of 2 close parentheses.

Solution:

It is given that square root of 2 open parentheses 5 minus 3 square root of 2 close parentheses

We can write it as √2(5 - 3√2)

Using the multiplicative distributive property

√2(5 - 3√2) = 5√2 - 3√2√2 = 5√2 - 3 × 2 = 5√2 - 6

Therefore, by simplifying we get (5√2 - 6).

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Simplify square root of 5 open parentheses 10 minus 4 square root of 2 close parentheses.

Summary:

Simplifying square root of 5 open parentheses 10 minus 4 square root of 2 close parentheses we get (10√5 - 4√10).