Question

Do the following :-
$2 \sqrt{3} + \sqrt{27}$
$\sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5}$
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Answer 1

$\huge{\bold{SOLUTION:-}}$$<b>$

Addition and subtraction of two surds is possible if they are similar i.e. the radicand and the order of radicand are same and the integral part of the surds can be different

1) $2 \sqrt{3} + \sqrt{27}$

$2 \sqrt{3} + 3 \sqrt{3}$

$(2 + 3) \sqrt{3}$

$\boxed{5 \sqrt{3}}$

2)$\sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5}$

$3 \sqrt{5} - 3 \times 2 \sqrt{5} + 4 \sqrt{5}$

$3 \sqrt{5} - 6 \sqrt{5} + 4 \sqrt{5}$

$\boxed{\sqrt{5}}$

Answer 2

1.)

$\large{2 \sqrt{3} + \sqrt{27} }$

$\large{2 \sqrt{3} +3 \sqrt{3} }$

$= \large{ \boxed{5 \sqrt{3} }}$

2.)

$\large{ \sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5} }$

$\large{ 3\sqrt{5} - 6 \sqrt{5} + 4 \sqrt{5} }$

$\large{7 \sqrt{5} - 6 \sqrt{5} }$

$= \large{ \boxed{ \sqrt{5} }}$

THANKS