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Step-4

Title: Adding and Subtracting Radicals

Grade: 8-b Lesson: S1-L6

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

Lesson Steps

Discussion: Step1 Step2 Step3 Step4 Step5

Step	Type	Explanation	Answer
1	Problem	Simplify the following expression: \$ - sqrt( 625) + \sqrt(64)\$.
2	Step	The given expression	\$ - sqrt( 625) + \sqrt(64)\$
3	Step	Simplify first radical separately:	\$\sqrt(625) = 25\$ (since \$\sqrt(625) = \sqrt(25^2) = 25\$)
4	Step	Simplify second radical separately:	\$\sqrt(64) = 8\$ (since \$ \sqrt(64) = \sqrt(8^2) = 8\$)
5	Step	Substitute the simplified values into the expression:	⇒ - 25 + 8 ⇒ -17
6	Step	Therefore, the simplified form of the expression \$ - sqrt( 625) + \sqrt(64)\$ is - 17.
7	Choice.A	After evaluating the square roots and performing the arithmetic, we obtain -17, which matches option A	-17
8	Choice.B	It is suggested the answer is −30, which does not correspond to the result of -25 + 8. The correct simplification yields -17, not -30	-30
9	Choice.C	Wrong: Because the correct simplified result is -17, not 33. There is no way the expression -25 + 8 can result in 33	33
10	Choice.D	15.The result we got is −17, which is not equal to 15. Therefore, option D is not correct	15
11	Answer	Option	A
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Simplify the following expression: \$ - sqrt( 625) + \sqrt(64)\$.

Step

The given expression

\$ - sqrt( 625) + \sqrt(64)\$

Step

Simplify first radical separately:

\$\sqrt(625) = 25\$

(since \$\sqrt(625) = \sqrt(25^2) = 25\$)

Step

Simplify second radical separately:

\$\sqrt(64) = 8\$

(since \$ \sqrt(64) = \sqrt(8^2) = 8\$)

Step

Substitute the simplified values into the expression:

⇒ - 25 + 8

⇒ -17

Step

Therefore, the simplified form of the expression \$ - sqrt( 625) + \sqrt(64)\$ is - 17.

Choice.A

After evaluating the square roots and performing the arithmetic, we obtain -17, which matches option A

-17

Choice.B

It is suggested the answer is −30, which does not correspond to the result of -25 + 8. The correct simplification yields -17, not -30

-30

Choice.C

Wrong: Because the correct simplified result is -17, not 33. There is no way the expression -25 + 8 can result in 33

Choice.D

15.The result we got is −17, which is not equal to 15. Therefore, option D is not correct

Answer

Option

Sumup

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

Discussion: Step1 Step2 Step3 Step4 Step5