Simplify the following: 3√3 + 2√27 + 7/√3

Solution:

Given, the expression is 3√3 + 2√27 + 7/√3

We have to simplify the expression.

2√27 = 2√9 × 3

= 2(3√3)

= 6√3

Rationalising the denominator,

7/√3 = (7/√3) × (√3/√3)

= 7√3/3

3√3 + 2√27 + 7/√3 = 3√3 + 6√3 + 7√3/3

= √3(3 + 6 + 7/3)

= √3(9 + 7/3)

= √3(27+7)/3

= 34√3/3

Therefore, 3√3 + 2√27 + 7/√3 = 34√3/3

✦ Try This: Simplify the expression: 2√3 + 2√18 + 8/√3

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 9(v)

Simplify the following: 3√3 + 2√27 + 7/√3

Summary:

When an irrational and a rational number are added, the result or their sum is an irrational number only. The simplified form of 3√3 + 2√27 + 7/√3 is 34√3/3

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