Find the cube root of 38-17- 5

38+17√(5) =8+30+5√(5)+12√(5) =(√(5))^3+2^3+3×2×(√(5))^2+3×2^2×√(5) =(√(5)+2)^3 Hence, cube root of 38+17√(5) is √(5) +2 ...

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Byju's Answer

Standard VIII

Mathematics

Cube Root of a Cube Number Using Estimation

Find the cube...

Question

Find the cube root of
$38 + 17 \sqrt{5}$

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Solution

$38 + 17 \sqrt{5}$
$= 8 + 30 + 5 \sqrt{5} + 12 \sqrt{5}$
$= (\sqrt{5})^{3} + 2^{3} + 3 \times 2 \times (\sqrt{5})^{2} + 3 \times 2^{2} \times \sqrt{5}$
$= (\sqrt{5} + 2)^{3}$
Hence, cube root of $38 + 17 \sqrt{5}$ is $\sqrt{5} + 2$

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Find the cube root of38+17√5

38+17√5=8+30+5√5+12√5=(√5)3+23+3×2×(√5)2+3×22×√5=(√5+2)3Hence, cube root of 38+17√5 is √5+2

Find the cube root of
$38 + 17 \sqrt{5}$

$38 + 17 \sqrt{5}$
$= 8 + 30 + 5 \sqrt{5} + 12 \sqrt{5}$
$= (\sqrt{5})^{3} + 2^{3} + 3 \times 2 \times (\sqrt{5})^{2} + 3 \times 2^{2} \times \sqrt{5}$
$= (\sqrt{5} + 2)^{3}$
Hence, cube root of $38 + 17 \sqrt{5}$ is $\sqrt{5} + 2$