Question

3√2×4√2×12√32 =? (class 9th) please do a step by step answer​

Answer 1

Answer:

2 is the answer

${2}^{ \frac{1}{3} + \frac{1}{4} + \frac{5}{12} } = {2}^{ \frac{12}{12} } = {2}^{1} = 2$

Answer 2

Step-by-step explanation:

Given :-

³√2 × ⁴√2 × ¹²√32

To find :-

Simplify the expression ?

Solution :-

Given expression is ³√2 × ⁴√2 × ¹²√32

³√2 can be written as 2^(1/3)

⁴√2 can be written as 2^(1/4)

¹²√32 can be written as 32^(1/12)

32 = 2×2×2×2×2

=> 32^(1/12)

=> (2^5)^(1/12)

=> 2^(5/12)

LCM of 3 ,4 and 12 = 12

So,

2^(1/3) = 2^[(1/3)×4/4)]

=> 2^(1/3) = 2^(4/12)

2^(1/4) = 2^[(1/4)×(3/3)]

=> 2^(1/4) = 2^(3/12)

³√2 × ⁴√2 × ¹²√32

Given expression becomes

=> 2^(1/3) × 2^(1/4) × 2^(5/12)

=> 2^(4/12) × 2^(3/12) × 2^(5/12)

We know that

a^m × a^n = a^(m+n)

=> 2^[(4/12)+(3/12)+(5/12)]

=> 2^[(4+3+5)/12]

=> 2^(12/12)

=> 2^1

=> 2

Alternative method :-

Given expression is ³√2 × ⁴√2 × ¹²√32

=> 2^(1/3) × 2^(1/4) × 32^(1/12)

=> 2^(1/3) × 2^(1/4) × (2^5)^(1/12)

=> 2^(1/3) × 2^(1/4) × 2^(5/12)

=> 2^[(1/3)+(1/4)+(5/12)]

=> 2^[(4+3+5)/12)]

=> 2^(12/12)

=> 2^1

=> 2

Answer:-

The value of the expression

³√2 × ⁴√2 × ¹²√32 is 2

Used formulae:-

• 'nth root a' can be written as a^1/n

• a^m × a^n = a^(m+n)

• (a^m)^n = a^(mn)

• The symbol ^ represents "to the power of "