Question

7√3-5√2÷√48+√18
Rationalize​

Answer 1

Answer:

2/7

Step-by-step explanation:

Q. Rationalize :

$7 \sqrt{3} - 5 \sqrt{2} \div \sqrt{48} + \sqrt{18}$

Solution :

$7 \sqrt{3} - 5 \sqrt{2} \div \sqrt{48} + \sqrt{18}$

$(48 = 2 {}^{2} \times 2 {}^{2} \times 3) \\ ( 18 = 2 \times 3 {}^{2} )$

Replacing the square root of 48 and 18 with their factors, we get :

$7 \sqrt{3} - 5 \sqrt{2} \div \sqrt{2 {}^{2} \times 2 {}^{2} \times 3 } + \sqrt{2 \times 3 {}^{2} }$

Further we get :

$7 \sqrt{3} - 5 \sqrt{2} \div 4 \sqrt{3} + 3 \sqrt{2}$

Now we cancel the like radicals, we obtain :

$7 - 5 \div 4 + 3$

$= \frac{2}{7}$

Therefore the answer is 2/7

Answer 2

Answer:

= 7√3-5√2÷√48+√18

= 144 - 41 root 6 / 30

Step-by-step explanation:

given ( 7 root 3 - 5 root 2 ) / ( root 48 + root 18 )

= ( 7 root 3 - 5 root 2 ) / ( root 4×4×3 + root 3×3×2 )

= ( 7 root 3 - 5 root 2 ) / ( 4 root 3 + 3 root 2 )

/* Multiply numerator and denominator by , we get

/* Multiply numerator and denominator by , we get= ( 7 root 3 - 5 root 2 ) ( 4 root 3 - 3 root 2 ) / ( 4 root 3 + 3 root 2 ) ( 4 root 3 - 3 root 2 )

=( 28 × 3 - 21 root 6 - 20 root 6 + 15 × 2 ) / ( 4 root 3 )*2 - ( 3 root 2 )*2

= 84 - 41 root 6 + 30 / 48 - 18

= 114 - 41 root 6 / 30

/* Denominator rationalised .

/* Denominator rationalised .Therefore,

= ( 7 root 3 - 5 root 2 / ( root 48 + root 18 )

= 114 - 41 root 6 / 30 .

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