Question

if root2= 1,414, root3= 1.732 then find 4/3root3+2root2

Answer 1

Hiii friend,


✓2 = 1.414

And,


✓3 = 1.732


4/3✓3 + 2✓2


Rationalizing the denominator 3✓3 + 2✓2

=> 4/3✓3 + 2✓2 × 3✓3-2✓2/3✓3-2✓2


=> 4(3✓3-2✓2)/(3✓2+2✓2)(3✓3-2✓2)


=> 12✓3 - 8✓2/(3✓2)² - (2✓2)²

=> 12✓3 - 8✓2/18 - 8


=> 12✓3-8✓2/10


=> 2(6✓3-4✓2)/10

=> 6✓3-4✓2/5


=> 6 × 1.732 - 4 × 1.414/5


=> 10.392 - 5.656/5


=> 4.736/5



HOPE IT WILL HELP YOU...... :-)

Answer 2

Hope u like my process
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$\frac{4}{3 \sqrt{3} + 2 \sqrt{2} } + \frac{3}{3 \sqrt{3} - 2 \sqrt{2} } \\ = \frac{4(3 \sqrt{3} - 2 \sqrt{2} ) + 3(3 \sqrt{3} + 2 \sqrt{2} )}{(3 \sqrt{3} - 2 \sqrt{2} )(3 \sqrt{3} + 2 \sqrt{2} )} \\ = \frac{12 \sqrt{3} - 8 \sqrt{2} + 9 \sqrt{3} + 6 \sqrt{2} }{ {(3 \sqrt{3} )}^{2} - {(2 \sqrt{2} )}^{2} } \\ = \frac{21 \sqrt{3} - 2 \sqrt{2} }{27 - 8} = \frac{21 \times 1.732 - 2 \times 1.414}{19 } \\ = \frac{36.372 - 2.828}{19} = \frac{33.544}{19} \\ = 1.765$
Hope this is ur required answer
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