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a is the product of 3 and √2, b is the product of 2 and √3, and c is the product of 2 and √6. If x is the square of the sum of a and b, y is the product of 6 and (5 - c) and z is the product of square of 2 and square of 3, then what is the value of xy/z?

a is the product of 3 and √2, b is the product of 2 and √3, and c is the product of 2 and √6. If x is the square of the sum of a and b, y is the product of 6 and (5 - c) and z is the product of square of 2 and square of 3, then what is the value of xy/z? Correct Answer 1

Given:

a = 3√2, b = 2√3 and c = 2√6

x = (a + b)2

y = 6(5 - c)

z = 22 × 32 

Formula Used:

Using Algebraic formula:

(m + n)2 = m2 + n2 + 2mn

(m + n)(m - n) = m2 - n2

Calculation:

According to the question,

x is the square of the sum of a and b

⇒ x = (a + b)2

Substituting the value of a and b in the above equation, we get

⇒ x = (3√2 + 2√3)2 

⇒ x = (3√2)2 + (2√3)2 + 2(3√2)(2√3)

⇒ x = 18 + 12 + 12√6

⇒ x = 30 + 12√6

Also given that, y is the product of 6 and (5 - c)

y = 6(5 - c) = 6(5 - 2√6)

⇒ y = 30 - 12√6

And z = 22 × 32 = 36

The value of xy/z = /36

⇒ /36

⇒ (900 - 864)/36

⇒ 36/36 = 1

∴ The value of xy/z is 1.

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