Question

Simplify (√5+√2) the whole square

Answer 1

$(\sqrt{2}+\sqrt{5})^2\\=(\sqrt2)^2+(\sqrt5)^2+2\cdot(\sqrt2)(\sqrt5)\\= 2+5+2\sqrt{10}=7+2\sqrt{10}$ 

Answer 2

$\bf \red{( { \sqrt{5} + \sqrt{2} )}^{2} = 7 + 2 \sqrt{10}}$

Given:

• $( { \sqrt{5} + \sqrt{2} )}^{2}$

To find:

• Simplify.

Solution:

Identity to be used:

• $( {x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$
• $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$
• $( { \sqrt{a} )}^{2} = a$

Step 1:

Open the whole square as per Identity.

$( { \sqrt{5} + \sqrt{2}) }^{2} = ( { \sqrt{5}) }^{2} + ( { \sqrt{2} )}^{2} + 2 \sqrt{5} \sqrt{2}$

Step 2:

Simplify.

$( { \sqrt{5} + \sqrt{2} )}^{2} = 5 + 2 + 2 \sqrt{2 \times 5}$

or

$( { \sqrt{5} + \sqrt{2} )}^{2} = 7 + 2 \sqrt{10}$

Thus,

$\bf ( { \sqrt{5} + \sqrt{2} )}^{2} = 7 + 2 \sqrt{10}$

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