Question

1) (2√3+3√18-5√2)*√2+√24= 2) √(√5-2)^2 + √(√5-7)^2 + (3√2)^2

Answer 1

1)36.89897948556636
2)23.03188121493133

Answer 2

Let's solve these step by step.

1. (2√3 + 3√18 - 5√2) * √2 + √24:

First, let's simplify the terms inside the parentheses: 2√3 + 3√18 - 5√2

We know that: √3 = √(3) = √(3 * 1) = √(3) * √(1) = √(3) * 1 = √3 √18 = √(9 * 2) = √(9) * √(2) = 3√2 √2 = √(2) = √(2) * 1 = √2

Substitute these back into the expression: 2√3 + 3√18 - 5√2 = 2√3 + 3 * 3√2 - 5 * √2 = 2√3 + 9√2 - 5√2 = 2√3 + 4√2

Now, substitute this back into the main expression: (2√3 + 4√2) * √2 + √24

Distribute the √2: 2√3 * √2 + 4√2 * √2 + √24

Simplify: 2√(3 * 2) + 4√(2 * 2) + √24 = 2√6 + 4 * 2 + √24 = 2√6 + 8 + √24

Now, simplify √24: √24 = √(4 * 6) = √4 * √6 = 2√6

Substitute this back into the expression: 2√6 + 8 + 2√6 = 4√6 + 8.

2. √(√5 - 2)^2 + √(√5 - 7)^2 + (3√2)^2:

Let's simplify the inner expressions first:

√(√5 - 2)^2 = √(5 - 4√5 + 4) = √(9 - 4√5) √(√5 - 7)^2 = √(5 - 14√5 + 49) = √(54 - 14√5) (3√2)^2 = 9 * 2 = 18

Now plug these back into the expression:

√(9 - 4√5) + √(54 - 14√5) + 18

There isn't much simplification we can do in this case, so the expression remains as:

√(9 - 4√5) + √(54 - 14√5) + 18.