Question

Find a and b if 3+√27+√75=a+b√3

Answer 1

$3 + 3 \sqrt{3} + 5 \sqrt{3} = a + b \sqrt{3} \\ a = - b \sqrt{3 } + 3 + 8 \sqrt{3}$
for b put the value of a in equation

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

$\textsf{3 + √27 + √75 = a + b√3}$

$\bf \underline{To \: find-}$

$\textsf{the value of a and b in given equation.}$

$\bf \underline{Solution-}$

$\textsf{We have,}$

$\rm{3 + \sqrt{27} + \sqrt{75} }$

$\textsf{Here,}$

$\textsf{√27 can be written as √9×3 = 3√2.}$

$\textsf{√75 can be written as √25×3 = 5√3.}$

$\textsf{then,}$

$\rm{ \implies \: 3 + 3 \sqrt{3} + 5 \sqrt{3} }$

$\rm{ \implies \: 3 + (3 + 5) \sqrt{3} }$

$\rm{ \implies}3 + 8 \sqrt{3}$

$\rm \therefore \: 3 + 8 \sqrt{3} = a + b \sqrt{c}$

$\textsf{On comparing with RHS we notice that}$

$\textsf{the value of a = 3 and b = 8,}$