Question

The real number √2√32/√3 + 3/8 equals:

(a) √6
(b) √65
(c) √36
(d) √66
(e) √2/√33

Answer 1

The expression √(2√32/√3 + 3/8) simplifies to 2√(2/3) + √(3/8).

Step-by-step explanation:

The expression √(2√32/√3 + 3/8) can be simplified step by step.

First, let's simplify the terms inside the square root:

2√32/√3 + 3/8 = 2√(32/3) + 3/8 = 2√(32/3) + (3/8)√1

Next, let's simplify the square root of 32/3:

√(32/3) = √(32) / √(3) = 4√2 / √3

Now, let's substitute this value back into the original expression:

√(2√32/√3 + 3/8) = √(2(4√2 / √3) + (3/8)√1) = √(8√2 / √3 + 3/8)

Finally, let's combine the terms inside the square root:

√(8√2 / √3 + 3/8) = √(8√2 / √3) + √(3/8) = √(8/3)√2 + √(3/8) = 2√(2/3) + √(3/8)

Therefore, the expression simplifies to 2√(2/3) + √(3/8).