Question

Show that 3√27×3√125=3√27×125

Answer 1

Question :- Show that ³√27 × ³√125 = ³√(27×125) .

Solution :-

we know that, ⁿ√(a) is equal to (a)^ (1/n).

Solving LHS :-

→ ³√27 × ³√125

→ (27)^(1/3) × (125)^(1/3)

→ (3³)^(1/3) × (5³)^(1/3)

using (a^b)^c = (a)^(b*c) ,

→ (3)^(3 * 1/3) × (5)^(3 * 1/3)

→ (3)¹ × (5)¹

→ 3 × 5

→ 15.

Solving RHS :-

→ ³√(27 × 125)

→ (27 × 125)^(1/3)

→ (3³ × 5³)^(1/3)

using a^b × c^b = (a × c)^b

→ {(3 × 5)³}^(1/3)

→ {(15)³}^(1/3)

→ (15³)^(1/3)

Now, using (a^b)^c = (a)^(b*c)

→ (15)^(3 * 1/3)

→ 15¹

→ 15.

LHS = RHS. (Hence, Proved).

Learn More :-

(3/2)^-3 को किस संख्या से भाग दिया जाए कि भागफल (4/9)^-2

प्राप्त हो?

https://brainly.in/question/21653194

Answer 2

Answer:

$\sqrt[3]{27} \times \sqrt[3]{125} = \sqrt[3]{27 \times 125}$

${3}^{3} \times {5}^{3} = {3}^{3} \times {5}^{3}$

$( {3 \times 5})^{3} = ({3 \times 5)}^{3}$

${15}^{3} = {15}^{3}$

hope it will help you