Question

$5 \sqrt{2} + 2 \sqrt{8 } - 3 \sqrt{32} + 4 \sqrt{128} Plain form$
​

Answer 1

Answer:

29√2

Explanation:

$5 \sqrt{2} + 2 \sqrt{8 } - 3 \sqrt{32} + 4 \sqrt{128} Plain form$

____________________

i) √8 = √(2×2×2) = 2√2

ii) √32 = √(2×2×2×2×2)=4√2

iii)√128=√(8×8×2) = 8√2

____________________

= 5√2+2(2√2)-3(4√2)+4(8√2)

= 5√2+4√2-12√2+32√2

=(5+4-12+32)√2

= 29√2

••••

Answer 2

5√2 + 2√8 - 3√32 + 4√128

Solve the Square roots to factorize in simplest form

$\bf\huge\sqrt{8} = \sqrt{2\times 2\times 2} = 2\sqrt{2}$    

$\bf\huge\sqrt{32} = \sqrt{2\times 2\times 2\times 2\times 2} = 4\sqrt{2}$    

$\bf\huge\sqrt{128} = \sqrt{8\times 8\times 2} = 8\sqrt{2}$    

Now substitute the value that we get above ↑

= 5√2 + 2(2 √2) - 3(4√2) + 4(8√2)

= 5√2 + 4√2 - 12√2 + 32√2

= (5 + 4 - 12 + 32)√2

$\bf\huge\bf\huge{\boxed{\bigstar{{29\sqrt{2}}}}}$