Studdy AI Logo
Math  /  Algebra

QuestionB=(3+5)2−(5+7)2−132B=(\sqrt{3+\sqrt{5}})^{2}-\sqrt{(\sqrt{5}+7)^{2}}-\sqrt{13^{2}}

Studdy Solution

STEP 1

1. The expression involves nested square roots and powers.
2. Simplification will involve evaluating powers and square roots.
3. The expression can be simplified step-by-step to find the equivalent counting number.

STEP 2

1. Simplify each term in the expression individually.
2. Combine the simplified terms to find the final result.

STEP 3

Simplify the first term (3+5)2(\sqrt{3+\sqrt{5}})^{2}.
Since squaring a square root cancels out the square root, we have:
(3+5)2=3+5(\sqrt{3+\sqrt{5}})^{2} = 3 + \sqrt{5}

STEP 4

Simplify the second term (5+7)2\sqrt{(\sqrt{5}+7)^{2}}.
Since the square root and the square cancel each other, we have:
(5+7)2=5+7\sqrt{(\sqrt{5}+7)^{2}} = \sqrt{5} + 7

STEP 5

Simplify the third term 132\sqrt{13^{2}}.
Since the square root and the square cancel each other, we have:
132=13\sqrt{13^{2}} = 13

STEP 6

Combine the simplified terms:
The expression becomes:
B=(3+5)−(5+7)−13B = (3 + \sqrt{5}) - (\sqrt{5} + 7) - 13
Simplify by combining like terms:
First, simplify 3+5−53 + \sqrt{5} - \sqrt{5}:
3+5−5=33 + \sqrt{5} - \sqrt{5} = 3
Then, subtract the remaining terms:
3−7−13=3−20=−173 - 7 - 13 = 3 - 20 = -17
Thus, the equivalent counting number for the expression is:
−17\boxed{-17}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord