Simplify the given surd- -45 - 3-20 - 3-5-

The given surds can be simplified as follows: √( 45 ) 3√( 20 ) +3√( 5 ) =√( 9× 5 ) 3√( 4× 5 ) +3√( 5 ) =3√( 5 ) (3× 2√( 5 ) )+3√( 5 ) =3√( 5 ) 6√( ...

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Byju's Answer

Standard IX

Mathematics

(x±a)(x±b) = x²±(a+b)x+ab.

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Question

Simplify the given surd: $\sqrt{45} - 3 \sqrt{20} + 3 \sqrt{5}$ .

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Solution

The given surds can be simplified as follows:
$\sqrt{45} - 3 \sqrt{20} + 3 \sqrt{5} = \sqrt{9 \times 5} - 3 \sqrt{4 \times 5} + 3 \sqrt{5} = 3 \sqrt{5} - (3 \times 2 \sqrt{5}) + 3 \sqrt{5}$
$= 3 \sqrt{5} - 6 \sqrt{5} + 3 \sqrt{5} = \sqrt{5} (3 - 6 + 3)$
$= \sqrt{5} (6 - 6) = 0 \times \sqrt{5} = 0$

Hence, $\sqrt{45} - 3 \sqrt{20} + 3 \sqrt{5} = 0$ .

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Simplify the given surd: √45−3√20+3√5.

The given surds can be simplified as follows:√45−3√20+3√5=√9×5−3√4×5+3√5=3√5−(3×2√5)+3√5=3√5−6√5+3√5=√5(3−6+3)=√5(6−6)=0×√5=0Hence, √45−3√20+3√5=0.

Simplify the given surd: $\sqrt{45} - 3 \sqrt{20} + 3 \sqrt{5}$ .