Question

The value of root(17+ 4 root13) - root(17 - 4 root13) is
(A) 2
(C) 4
(B) 3
(D) 5​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The value of

$\sf{ \sqrt{17 + 4 \sqrt{13} } - \sqrt{17 - 4 \sqrt{13} } }$

(A) 2

(B) 3

(C) 4

(D) 5

EVALUATION

Here the given expression is

$\sf{ \sqrt{17 + 4 \sqrt{13} } - \sqrt{17 - 4 \sqrt{13} } }$

We solve it as below

$\sf{ \sqrt{17 + 4 \sqrt{13} } - \sqrt{17 - 4 \sqrt{13} } }$

$\sf{ = \sqrt{13 + 4 + 4 \sqrt{13} } - \sqrt{13 + 4- 4 \sqrt{13} } }$

$\sf{ = \sqrt{ {( \sqrt{13} )}^{2} + {2}^{2} + 2 \times \sqrt{13} \times 2} - \sqrt{ {( \sqrt{13} )}^{2} + {2}^{2} - 2 \times \sqrt{13} \times 2}}$

$\sf{ = \sqrt{ {( \sqrt{13} + 2)}^{2} } - \sqrt{ {( \sqrt{13} - 2)}^{2} }}$

$\sf{ = ( \sqrt{13} + 2) - ( \sqrt{13} - 2)}$

$\sf{ = \sqrt{13} + 2 - \sqrt{13} + 2}$

$\sf{ = 4}$

FINAL ANSWER

Hence the correct option is (C) 4

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