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Powers and Roots Practice Test 2

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Question : 3 of 40

Marks: +1, -0

Simplify :

\sqrt{41-\sqrt{21+\sqrt{19-\sqrt{9}}}}

6.4
6
5
3

Solution:

Concept:

Simplify nested square roots by evaluating from the innermost root outward.

Explanation:

Start with the innermost root:

\sqrt{9}=3

.

Then

19-\sqrt{9}=19-3=16

.

So

\sqrt{16}=4

.

Next,

21+\sqrt{19-\sqrt{9}}=21+4=25

.

So

\sqrt{25}=5

.

Then

41-\sqrt{21+\sqrt{19-\sqrt{9}}}=41-5=36

.

Finally,

\sqrt{36}=6

.

Answer:

The simplified value is

6

, so the correct option is B.

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