The value of 3-2- 7-6- 5-18 is

3√(2)× 7√(6)× 5√(18) ⇒ 3 × (2)^1/3× 7 × (6)^1/3× 5 × (18)^1/3 Grouping with same powers: ⇒ 105 × (2 × 6 × 18)^1/3 ⇒ 105 × (2× 6 × 6 × 3)^1/3 ⇒ [105] × [6]^3 ×1/ ...

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Byju's Answer

Standard VIII

Mathematics

Expanding a Rational Number Using Powers

The value of ...

Question

The value of $3 \sqrt[3]{2} \times 7 \sqrt[3]{6} \times 5 \sqrt[3]{18}$ is

545

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400

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500

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630

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Solution

The correct option is D 630
$3 \sqrt[3]{2} \times 7 \sqrt[3]{6} \times 5 \sqrt[3]{18}$
$\Rightarrow 3 \times (2)^{\frac{1}{3}} \times 7 \times (6)^{\frac{1}{3}} \times 5 \times (18)^{\frac{1}{3}}$
Grouping with same powers:
$\Rightarrow 105 \times (2 \times 6 \times 18)^{\frac{1}{3}}$
$\Rightarrow 105 \times (2 \times 6 \times 6 \times 3)^{\frac{1}{3}}$
$\Rightarrow [105] \times [6]^{3 \times \frac{1}{3}} = 105 \times 6 = 630$

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Similar questions

Question 6

Which of the following expressions show that rational numbers are associative under multiplication.
(a) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5}$
(b) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = \frac{2}{3} \times (\frac{3}{5} \times \frac{- 6}{7})$
(c) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{3}{5} \times \frac{2}{3}) \times \frac{- 6}{7}$
(d) $(\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5} = (\frac{- 6}{7} \times \frac{2}{3}) \times \frac{3}{5}$

Q. Find the value of:

(1) 3⁶
(2) 6³
(3) 2⁶
(4) 1⁸
(5) 5⁴
(6) 4³
(7) 10⁵
(8) 10⁷
(9) 7⁴
(10) 8²

Q. The value of

3 \sqrt[3]{2} \times 7 \sqrt[3]{6} \times 5 \sqrt[3]{18}

is:

Q. The simplified value of

[18 \div 6 + {2 \times (8 - 7 \times 3) + 17 \times 5}]

The value of $3 \times (2)^{\frac{1}{3}} \times 7 \times (6)^{\frac{1}{3}} \times 5 \times (18)^{\frac{1}{3}}$ is

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The value of 33√2×73√6×53√18 is

The correct option is D 63033√2×73√6×53√18 ⇒3×(2)13×7×(6)13×5×(18)13 Grouping with same powers: ⇒105×(2×6×18)13 ⇒105×(2×6×6×3)13 ⇒[105]×[6]3×13=105×6=630

The value of $3 \sqrt[3]{2} \times 7 \sqrt[3]{6} \times 5 \sqrt[3]{18}$ is