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Gekata [30.6K]
3 years ago
14

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b

Baseline EndRoot a = 3, b = 2 a = 2, b = 3 a = 3, b = 4 a = 4, b = 3
Mathematics
2 answers:
kramer3 years ago
4 0

Option C: a=3, b=4 is the value of a and b

Explanation:

Given that the expression \sqrt{648}=\sqrt{2^a\times3^b}

We need to determine the value of a and b

Let us consider the term \sqrt{648} and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

648=2 \cdot 324

324 divides by 2,

648=2 \cdot 2 \cdot 162

162 divides by 2,

648=2 \cdot 2 \cdot 2 \cdot 81

81 divides by 3,

648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27

27 divides by 3,

648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9

9 divides by 3,

648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3

Thus, we have,

\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}

Therefore, equating the powers of 2 and 3, we get,

a=3, b=4

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

mixer [17]3 years ago
4 0

Answer:

c

Step-by-step explanation:

c c c c c c c c c c c c c c c c c c c c c c c c c c

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