Square Roots and Factoring

[tonebeeze]

The value of √(2^5 * 3^2 * 5^4) is between which of the following pairs of numbers?

a. 0 and 100
b. 100 and 200
c. 200 and 300
d. 300 and 400
e. 400 and 500

OA = E

[anshumishra]

The value of √(2^5 * 3^2 * 5^2) is between which of the following pairs of numbers?

a. 0 and 100
b. 100 and 200
c. 200 and 300
d. 300 and 400
e. 400 and 500

OA = E

√(2^5 * 3^2 * 5^2) = 4*3*5*√2 = 60√2 ~= 84
So, ans. should be A.

[tonebeeze]

The square root sign is meant to cover all the terms under the radical, so 2^5 * 3^2 * 5^2 are intended to be under the radical. It is really hard to write out equations on here. Thus the square root of 180,000 should be between 400-500. So the answer is E

[tonebeeze]

Anu, you were correct...I wrote the problem out incorrectly initially. I wrote 5^2 instead of 5^4. I apologize. I edited the equation in the initial post:
√(2^5 * 3^2 *5^4)

[anshumishra]

Anu, you were correct...I wrote the problem out incorrectly initially. I wrote 5^2 instead of 5^4. I apologize. I edited the equation in the initial post:
√(2^5 * 3^2 *5^4)

No problem, it happens. Glad that you got the answer.