Question

simplify root 48 + root 32 / root 27 + root 18​

Answer 1

Answer:

4/3

Step-by-step explanation:

The question is,

(√48 + √32) / (√27 + √18) = ?

Lets take left hand side (L.H.S) and solve it,

=> L.H.S = (√48 + √32 ) / (√27 + √18 )

=> L.H.S = (4√3 + 4√2) / (3√3 + 3√2)

=> L.H.S = {4(√3 + √2)} / {3(√3 + √2)}

=> L.H.S = 4/3

●SO THE CORRECT ANSWER IS 4/3

●Hope my answer helped.

Answer 2

Solution!!

$\sf \to \dfrac{\sqrt{48}+\sqrt{32}}{\sqrt{27}+\sqrt{18}}$

Simplify the radical expressions.

$\sf \to \dfrac{4\sqrt{3}+4\sqrt{2}}{3\sqrt{3}+3\sqrt{2}}$

Factor out 3 from the expressions.

$\sf \to \dfrac{4\sqrt{3}+4\sqrt{2}}{3(\sqrt{3}+\sqrt{2})}$

Factor out 4 from the expressions.

$\sf \to \dfrac{4(\sqrt{3}+\sqrt{2})}{3(\sqrt{3}+\sqrt{2})}$

Reduce the fraction with $\sf \sqrt{3}+\sqrt{2}$.

$\sf \to \dfrac{4}{3}$

Convert the improper fraction into mixed fraction or decimals.

$\sf \to 1\dfrac{1}{3}\:or\:1.33$

Note:- Never leave your answer as an improper fraction. The examiner may deduct your marks.

Some rules:-

→ $\sf \sqrt{a\times b}=\sqrt{a}\sqrt{b}$

→ $\sf \sqrt{a}\sqrt{a}=a$

→ $\sf a\sqrt{b}\times a\sqrt{b}=a^{2}b$

→ $\sf \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$

→ $\sf a\sqrt{b}\pm c\sqrt{b}=(a\pm c)\sqrt{b}$