Arrange -2-3 and -5 in ascending order-

L.C.M. of 2, 3, 4= 12 ⇒ #160; √(2)=√(2^6)=√(64) ⇒√(3)=√(3^4)=√(81) ⇒√(5)=√(5^3)=√(125) Now, 64 lt; 81 lt; 125 , ∴ # ...

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Byju's Answer

Standard IX

Mathematics

Irrational Numbers

Arrange √2,...

Question

Arrange $\sqrt{2}, \sqrt[3]{3}$ and $\sqrt[4]{5}$ in ascending order.

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Solution

L.C.M. of $2, 3, 4 = 12$
$\Rightarrow$ $\sqrt{2} = \sqrt[2 \times 6]{2^{6}} = \sqrt[12]{64}$
$\Rightarrow \sqrt[3]{3} = \sqrt[3 \times 4]{3^{4}} = \sqrt[12]{81}$
$\Rightarrow \sqrt[4]{5} = \sqrt[4 \times 3]{5^{3}} = \sqrt[12]{125}$
Now, $64 < 81 < 125$ ,
$∴$ $\sqrt[12]{64} < \sqrt[12]{81} < \sqrt[12]{125}$
$\Rightarrow \sqrt{2} < \sqrt[3]{3} < \sqrt[4]{5}$

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Arrange √2,3√3 and 4√5 in ascending order.

L.C.M. of 2,3,4=12⇒ √2=2×6√26=12√64⇒3√3=3×4√34=12√81⇒4√5=4×3√53=12√125Now, 64<81<125,∴ 12√64<12√81<12√125⇒√2<3√3<4√5

Arrange $\sqrt{2}, \sqrt[3]{3}$ and $\sqrt[4]{5}$ in ascending order.