Question

Root 3 minus root 2 whole square

Answer 1

Answer:

$(\sqrt3 - \sqrt2)^2 = 5 - 2\sqrt6$

Step-by-step explanation:

WKT : (a-b)² = a² - 2ab + b²

       = √3² - 2√3 × √2 + √2²

       = 3 - 2√6 + 2

       = 5 - 2√6

hence solved

Answer 2

As per the data in question

We have to find the whole square of given expression

Step-by-step explanation:

Root 3 minus root 2 whole square

Expression in mathematics:

${( \sqrt{3 } - \sqrt{2} )}^{2}$

Step-1:

Using identity:

(a-b)²=a²+b²-2×a×b

verbally - a minus b whole square

Both values are different but from the same function family.

Step -2:

Here ,

a= √3 and b=√2

Put the values in identity:

${( \sqrt{3} - \sqrt{2} )}^{2} = \\ { (\sqrt{3} )}^{2} + { (\sqrt{2}) }^{2} - 2 \times \sqrt{3} \times \sqrt{2}$

The whole square cancel out the root value ,

${( \sqrt{3} - \sqrt{2} )}^{2} =3 + 2 -2 \times \sqrt{3} \times \sqrt{2}$

Add the first two values i.e. 3 and 2

${( \sqrt{3} - \sqrt{2} )}^{2} =5 -2 \times \sqrt{3} \times \sqrt{2}$

Multiply the root values √3 and √2 ,

${( \sqrt{3} -\sqrt{2} )}^{2} =5-2 \times \sqrt{6}$

Or

Hence ,

we can rewrite as

${( \sqrt{3} - \sqrt{2} )}^{2} =5 - 2 \sqrt{6}$

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