Question

if the positive square root of √90+√80 and is multiple by root 2-1 then what is the value of the product raised to the power of 4​

Answer 1

Answer:

10

Step-by-step explanation:

Answer 2

Given :- if the positive square root of (√90 +√ 80) is multiplied by (√2-1) and the product is raised to the power of four the result would be ?

Solution :-

→ √90 + √80

→ √(9 * 10) + √(16 * 5)

→ √(3² * 10) + (4² * 5)

→ 3√10 + 4√5

→ (3*√2*√5) + (2*√2*√2*√5)

taking common ,

→ (√2 * √5)[3 + 2√2]

→ √10(3 + 2√2)

→ √10(2 + 1 + 2√2)

→ √10[(√2)² + (1)² + 2 * 1 * √2)]

comparing with (a² + b² + 2ab) = (a + b)²

→ √10[(√2 + 1)²]

now, we have given that, Positive square root of (√90 + √80) is multiply by (√2 - 1).

So,

→ +√[√10{(√2 + 1)²}] * (√2 - 1)

→ (10)^(1/4)(√2 + 1) * (√2 - 1)

using (a + b)(a - b) = a² - b²,

→ 10^(1/4) * { (√2)² - (1)²}

→ 10^(1/4) * (2 - 1)

→ 10^(1/4).

Now, given that, product is raised to the power of four.

Therefore,

→ {10^(1/4)}⁴

using (a^b)^c = (a)^( b * c) ,

→ (10)^(1/4 * 4)

→ (10)^(1)

→ 10 (Ans.)

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