What is the square root to 23 + 4{10} -10{2} - 8{5}?

Correct Answer is : 5−10+22{5} - {10} + 2{2}5−10+22

Correct Answer is : 5−10+22{5} - {10} + 2{2}5−10+22

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Algebra and Applications Test 3

Question : 5 of 25

Marks: +1, -0

23 + 4\sqrt{10} -10\sqrt{2} - 8\sqrt{5}

Solution:

Concept:

Express the given radical expression as a perfect square.

Explanation:

Let

a=\sqrt{5}

b=\sqrt{10}

, and

c=2\sqrt{2}

Then

a^2=5

b^2=10

, and

c^2=8

Now expand

(a-b+c)^2

(a-b+c)^2=a^2+b^2+c^2-2ab+2ac-2bc

Substitute the values:

=5+10+8-2\sqrt{5}\sqrt{10}+2\sqrt{5}(2\sqrt{2})-2\sqrt{10}(2\sqrt{2})

=23-10\sqrt{2}+4\sqrt{10}-8\sqrt{5}

So,

23+4\sqrt{10}-10\sqrt{2}-8\sqrt{5}=(\sqrt{5}-\sqrt{10}+2\sqrt{2})^2

Taking the square root gives:

\sqrt{23+4\sqrt{10}-10\sqrt{2}-8\sqrt{5}}=\sqrt{5}-\sqrt{10}+2\sqrt{2}

Answer:

\sqrt{5}-\sqrt{10}+2\sqrt{2}

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