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16 divide root 2 -35 divide root 50 -2 root 18 + 3 root 72​

User Bjrnt
by
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1 Answer

5 votes

Given:

The expression is:


(16)/(√(2))-(35)/(√(50))-2√(18)+3√(72)

To find:

The simplified form of the given expression.

Solution:

We have,


(16)/(√(2))-(35)/(√(50))-2√(18)+3√(72)

It can be written as:


=(16)/(√(2))-(35)/(√(25* 2))-2√(9* 2)+3√(36* 2)


=(16)/(√(2))-(35)/(5√(2))-2* 3√(2)+3* 6√(2)

Rationalizing the denominator, we get


=(16)/(√(2))* (√(2))/(√(2))-(35)/(5√(2))* (√(2))/(√(2))-6√(2)+18√(2)


=(16√(2))/(2)-(35√(2))/(5* 2)-6√(2)+18√(2)


=8√(2)-(7√(2))/(2)+12√(2)


=20√(2)-(7√(2))/(2)

Taking LCM, we get


=(40√(2)-7√(2))/(2)


=(33√(2))/(2)

Therefore, the simplified form of the given expression is
(33√(2))/(2).

User Hu
by
8.3k points

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