Question
The Product $\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{32}$ is equal to:
✓
Answer
- $2$
Solution:
$\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{32}$
$=\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{(2)^5}$
$=(2)^{\frac{1}{3}}\times(2)^{\frac{1}{4}}\times(2)^{\frac{5}{15}}$
$=(2)^{\frac{1}{3}+\frac{1}{4}+\frac{5}{12}}$
$=(2)^{\frac{4+3+5}{12}}$
$=(2)^{\frac{12}{12}}$
$=2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In the following, write the correct answer.
D is point on the side BC of a $\triangle\text{ABC}$ such that AD bisects Then.
→D is point on the side BC of a $\triangle\text{ABC}$ such that AD bisects Then.
-
BC = CD
-
BA > BD
-
BD > BA
-
CD > CA
The value of $7^{\frac{1}{2}}.8^{\frac{1}{2}}$ is:
→- $(28)^\frac{1}{2}$
- $(56)^\frac{1}{2}$
- $(14)^\frac{1}{2}$
- $(42)^\frac{1}{2}$
The graph of y = 5 is a line:
-
Making an intercept 5 on the x-axis.
-
Making an intercept 5 on the y-axis.
-
Parallel to the x-axis at a distance of 5 units from the origin.
-
Parallel to the y-axis at a distance of 5 units from the origin.
The diagonals AC and BD of a rectangle ABCD intersect each other at P. If $\angle\text{ABD}=50^\circ,$ then $\angle\text{DPC}=$
→- 70°
- 90°
- 80°
- 100°
In the given figure, AB > AC. If BO and CO are the bisectors of $\angle\text{B}$ and $\angle\text{C}$respectively, then:
→
- OB < OC
- OB = OC
- OB > OC
In figure, AB || CD || EF and GH || KL. The measure of $\angle\text{HKL},$ is:
→- 85°
- 135°
- 145°
- 215°
If $\frac{3^{2\text{x}-8}}{225}=\frac{5^3}{5^{\text{x}}},$ then x =
→Two coins are tossed 1000 times and the outcomes are recorded as given below:
Now, if two coins are tossed at random, what is the probability of getting at most one head?
→|
Number of heads
|
2
|
1
|
0
|
|
Frequency
|
200
|
550
|
250
|
- $\frac{3}{4}$
- $\frac{4}{5}$
- $\frac{1}{4}$
- $\frac{1}{5}$
$\text{ABCD}$ is a rectangle with $O$ as any point in its interior. If $\text{ar}(\triangle\text{AOD})=3\text{cm}^2$ and $\text{ar}(\triangle\text{ABOC})=6\text{ cm}^2,$ then area of rectangle $\text{ABCD}$ is:
→