Question

arrange in ascending order ³√4, √3 ,⁴√6​
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Answer 1

Before we solve:-

Exponent was invented because it simplifies the calculation. Here, we are using the properties of exponent to solve the question. If we apply equal power, it won't rearrange the order.

So, let's do it!

What's used:-

Exponent

Solution:-

According to the power rule, the three numbers are $2^{\frac{2}{3} },\ 3^{\frac{1}{2} },\ 6^{\frac{1}{4} }$ respectively.

Let's consider comparing the numbers with inequality. Here, we will use the exponent $12$.

Then, now numbers are

• $(2^{\frac{2}{3} })^{12}=2^{8}=256$
• $(3^{\frac{1}{2} })^{12}=3^{6}=729$
• $(6^{\frac{1}{4} })^{12}=6^3=216$

If we compare the numbers we get $6^3<2^8<3^6$. This inequality holds for the previous numbers.

So, the result is $\sqrt[4]{6} <\sqrt[3]{4} <\sqrt{3}$, and the numbers are in ascending order. We're done!

Answer 2

$\sqrt[3]{9} = 6 \\ \sqrt{3} = 1.723 \\ \sqrt[4]{6} = 9.797 \\ in \: \: assending \: \: oder \\ \\ \sqrt{3} = 1.732 \\ \sqrt[3]{9} = 6 \\ \sqrt[4]{6} = 9.797$