Simplify the following: ⁴√81 - 8 ³√216 +15 ⁵√32 +√225
Solution:
Given, the expression is \(\sqrt[4]{81}-8\sqrt[3]{216}+15\sqrt[5]{32}+\sqrt{225}\)
We have to simplify the expression.
\(\sqrt[4]{81}=(81)^{\frac{1}{4}}=(3^{4})^{\frac{1}{4}}=3\)
\(\sqrt[3]{216}=(216)^{\frac{1}{3}}=(6^{3})^{\frac{1}{3}}=6\)
\(\sqrt[5]{32}=(32)^{\frac{1}{5}}=(2^{5})^{\frac{1}{5}}=2\)
√225 = 15
Now, \(\sqrt[4]{81}-8\sqrt[3]{216}+15\sqrt[5]{32}+\sqrt{225}\) = 3 - 8(6) + 15(2) + 15
= 3 - 48 + 30 + 15
= 3 - 48 + 45
= 48 - 48
= 0
Therefore, \(\sqrt[4]{81}-8\sqrt[3]{216}+5\sqrt[5]{32}+\sqrt{225}\) = 0
✦ Try This: Simplify the expression: Simplify the following: (√2 + √5)²
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 9(vii)
Simplify the following: ⁴√81 - 8 ³√216 +15 ⁵√32 +√225
Summary:
Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The simplified form is 0
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