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Title: Square roots and cube roots

Grade: 8-a Lesson: S1-L5

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	The difference between the square root and cube root of the number \$125 times 512\$ is?
2	Step	The given square and cube roots is	\$125 times 512\$
3	Step	Let’s calculate the product first:	\$125 times 512\$ = 64000
4	Step	Now, let’s find the square root	Square root of 64000: \$\sqrt(64000)\$ = 252.982
5	Step	Then find the cube root	Cube root of 64000: \$root(3)(64000)\$ = 40
6	Step	Finally calculate the difference between square root and cube root is	252.982 - 40 = 212.982
7	Step	The difference between the square root and cube root of the number \$125 times 512\$ is 212.982.
8	Choice.A	Wrong: It doesn’t represent the correct difference between the square root and the cube root of the given number	221.829
9	Choice.B	States the difference as 212.982, which matches our calculation. So, option B is correct	212.982
10	Choice.C	Option C, 212.289, is not correct because it does not match the calculated difference	212.289
11	Choice.D	States the difference as 221.982, which is incorrect according to our calculation	221.982
12	Answer	Option	B
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

The difference between the square root and cube root of the number \$125 times 512\$ is?

Step

The given square and cube roots is

\$125 times 512\$

Step

Let’s calculate the product first:

\$125 times 512\$ = 64000

Step

Now, let’s find the square root

Square root of 64000:
\$\sqrt(64000)\$ = 252.982

Step

Then find the cube root

Cube root of 64000:
\$root(3)(64000)\$ = 40

Step

Finally calculate the difference between square root and cube root is

252.982 - 40 = 212.982

Step

The difference between the square root and cube root of the number \$125 times 512\$ is 212.982.

Choice.A

Wrong: It doesn’t represent the correct difference between the square root and the cube root of the given number

221.829

Choice.B

States the difference as 212.982, which matches our calculation. So, option B is correct

212.982

Choice.C

Option C, 212.289, is not correct because it does not match the calculated difference

212.289

Choice.D

States the difference as 221.982, which is incorrect according to our calculation

221.982

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?