Simplify : (1³ + 2³ + 3³)1/2
Solution:
Given, the expression is \((1^{3}+2^{3}+3^{3})^{\frac{1}{2}}\)
We have to simplify the expression.
(1)³ = 1
(2)³ = 8
(3)³ = 27
So, (1³ + 2³ + 3³) = 1 + 8 + 27
= 9 + 27
= 36
\((1^{3}+2^{3}+3^{3})^{\frac{1}{2}}=(36)^{\frac{1}{2}}\)
= √36
= 6
Therefore, \((1^{3}+2^{3}+3^{3})^{\frac{1}{2}}\) = 6
✦ Try This: Simplify: \((1^{3}+2^{3}+3^{3}+4^{3})^{\frac{1}{2}}\)
Given, the expression is \((1^{3}+2^{3}+3^{3}+4^{3})^{\frac{1}{4}}\)
We have to simplify the expression.
(1)³ = 1
(2)³ = 8
(3)³ = 27
(4)³ = 64
So, (1³ + 2³ + 3³ + 4³) = 1 + 8 + 27 + 64
= 9 + 27 + 64
= 100
\((1^{3}+2^{3}+3^{3}+4^{3})^{\frac{1}{2}}=(100)^{\frac{1}{2}}\)
= √100
= 10
Therefore, \((1^{3}+2^{3}+3^{3}+4^{3})^{\frac{1}{2}}\) = 10
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 14(i)
Simplify : (1³ + 2³ + 3³)1/2
Summary:
A number is called a rational number, if it can be written in the form p/q, where p and q are integers and q ≠ 0. The simplified form of (1³ + 2³ + 3³)1/2 is 6
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