Question

Test weather the given numbers are perfect cubes or not? 8000​

Answer 1

Answer:

your step by step solution is in the above attached pic

Answer 2

$\huge{ \underline{ \bf{To \: verify \: : }}}$

• 8000 is a perfect cube or not

$\huge{ \underline{ \underline{ \bf{Solution \: : - }}}}$

Do L.C.M. of 8000

$\underline{2 \mid8000} \\ \underline{ 2 \mid4000} \\ \underline{ 2 \mid2000} \\ \underline{ 2 \mid1000} \\ \underline{ 2 \mid0500} \\ \underline{ 2 \mid0250} \\ \underline{ 5 \mid0125} \\ \underline{ 5 \mid0025 }\\ \underline{ 5 \mid0005} \\ \: \: \: \: \mid0001$

Now put the values

$8000 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5$

Now group all the numbers in each set 3 numbers, like,

$\underbrace{2 \: \: 2 \: \: 2} \: \: \underbrace{ 2 \: \: 2 \: \: 2} \: \: \underbrace{5 \: \: 5 \: \: 5}$

$= 2 \times 2 \times 5$

$= 20$

Therefore, 8000 is a perfect cube.

$8000 = 20 \times 20 \times 20$