Solve Nested Square Roots: √√(100/25) × √√25 Multiplication Problem

Question

Solve the following exercise:

1002525= \sqrt{\sqrt{\frac{100}{25}}}\cdot\sqrt{\sqrt{25}}=

Video Solution

Solution Steps

00:00 Solve the following problem
00:04 Break down the fraction to 10 divided by 5 squared
00:11 Break down 25 to 5 squared
00:17 The square root of any number (X) squared cancels out the square
00:28 We'll apply this formula to our exercise
00:50 The square root of a fraction (A divided by B)
00:53 Equals the square root of the numerator (A) divided by the square root of the denominator (B)
00:56 We'll apply this formula to our exercise
01:02 Simplify wherever possible
01:05 This is the solution

Step-by-Step Solution

To solve this problem, let's evaluate the expression 1002525 \sqrt{\sqrt{\frac{100}{25}}} \cdot \sqrt{\sqrt{25}} step-by-step.

Step 1: Simplify 10025\sqrt{\frac{100}{25}}.
We calculate 10025\frac{100}{25}, which simplifies to 4. Therefore, 10025=4=2\sqrt{\frac{100}{25}} = \sqrt{4} = 2.

Step 2: Now find 4\sqrt{\sqrt{4}}.
4=2\sqrt{4} = 2, so 2\sqrt{2} remains as it is.

Step 3: Simplify 25\sqrt{\sqrt{25}}.
Note that 25=5\sqrt{25} = 5. Therefore, 25=5\sqrt{\sqrt{25}} = \sqrt{5}.

Step 4: Combine the results:
The expression simplifies to 25\sqrt{2} \cdot \sqrt{5}, which is equal to 25=10\sqrt{2 \cdot 5} = \sqrt{10}.

Thus, the final result of the expression is 10\sqrt{10}.

The correct choice from the options provided is: 10 \sqrt{10} .

Answer

10 \sqrt{10}