Question

3³√64 +2√18- 3√50*⁴√625

Answer 1

................... ....

Answer 2

Let's simplify the expression step by step:

1. 3³√64: This means taking the cube root of 64, which is 4, as 4 × 4 × 4 = 64.

2. 2√18: This means taking the square root of 18. We can break it down as follows: √18 = √(9 × 2) = √9 × √2 = 3√2

3. 3√50: This means taking the cube root of 50. We can't simplify it further since 50 is not a perfect cube.

4. ⁴√625: This means taking the fourth root of 625, which is 5, as 5 × 5 × 5 × 5 = 625.

Now, let's put it all together and simplify the expression:

3³√64 + 2√18 - 3√50 * ⁴√625

= 4 + 2(3√2) - 3√50 * 5

= 4 + 6√2 - 15√50

At this point, we should try to simplify the radicals further. To do that, we need to find perfect squares that are factors of 2 and perfect squares that are factors of 50.

Factors of 2: 1, 2 (both are perfect squares)

Factors of 50: 1, 2, 5, 10, 25, 50 (10 and 25 are perfect squares)

Now, let's rewrite the expression with simplified radicals:

= 4 + 6√2 - 15√(25 × 2)

= 4 + 6√2 - 15(√25 × √2)

= 4 + 6√2 - 15(5√2)

= 4 + 6√2 - 75√2

Now, we can combine the like terms (terms with the same radical):

= (4 - 75)√2

= -71√2

So the simplified expression is -71√2.