Question

The value of √48 + √32 / √27 + √18 is​

Answer 1

48=6.93 + 32=5.66 + 27=5.20+ 18=4.24 =22.03

Answer 2

$\large\underline{\sf{Solution-}}$

Consider,

$\rm :\longmapsto\:\dfrac{ \sqrt{48} + \sqrt{32} }{ \sqrt{27} + \sqrt{18} }$

$\rm :\longmapsto\: = \: \dfrac{ \sqrt{4 \times 4 \times 3} + \sqrt{4 \times 4 \times 2} }{ \sqrt{3 \times 3 \times 3} + \sqrt{3 \times 3 \times 2} }$

$\rm :\longmapsto\: = \dfrac{4 \sqrt{3} + 4 \sqrt{2} }{3 \sqrt{3} + 3 \sqrt{2} }$

$\rm :\longmapsto\: = \: \dfrac{4 \: \: \cancel{( \sqrt{3} + \sqrt{2})}}{3 \: \: \cancel{( \sqrt{3} + \sqrt{2})}}$

$\rm :\longmapsto\: = \: \dfrac{4}{3}$

$\bf\implies \: \boxed{ \rm \: \dfrac{ \sqrt{48} + \sqrt{32} }{ \sqrt{27} + \sqrt{18} } = \dfrac{4}{3} }$

Additional Information :-

What are irrational numbers?

• Irrational numbers are the real numbers that cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio, such as a/b, where a and b are integers, q≠0.

• The decimal expansion of an irrational number is neither terminating nor recurring. 

• Irrational numbers are expressed usually in the form of R\Q, where the backward slash symbol denotes ‘set minus’. it can also be expressed as R – Q, which states the difference of set of real numbers and set of rational numbers.

• For example, √2, √3, √5, etc., are irrational

What is a Rational Number?

• A rational number can be defined as any number which can be represented in the form of p/q where q ≠ 0.  

• The decimal form of rational numbers may be either terminating decimal or the repeating decimal.