Question

simplify √72 +√ 800 -√18

Answer 1

√72+√800-√18

→ = √6×6×2+√20×20×2-√2×3×3

→ = 6√2+20√2-3√2

→ = 26√2-3√2

→ = 23√2

Hope it helps

Answer 2

Answer:

$\sqrt{72}+\sqrt{800}-\sqrt{18}$

=$23\sqrt{2}$

Step-by-step explanation:

i)Resolving numbers 72, 800 and into prime factors, we get

72 = 2×2×2×3×3 =2²×2×3²

800 = 2×2×2×2×2×5×5=2⁴×2×5²

18 = 2×3×3=2×3²

Now ,

ii) Find square root of above Numbers:

a)$\sqrt{72}</p><p>=\sqrt{2^{2}\times 3^{2}\times 2}$

= $2\times 3 \sqrt{2}$

= $6\sqrt{2}$ ----(1)

b) $\sqrt{800} = \sqrt{2^{4}\times 2 \times 5^{2}}$

= $2^{2}\times 5 \sqrt{2}$

= $20\sqrt{2}$ -----(2)

c)$\sqrt{18} = \sqrt{2 \times 3^{2}}$

=$3\sqrt{2}$---(3)

Therefore,

$\sqrt{72}+\sqrt{800}-\sqrt{18}$

=$6\sqrt{2}+20\sqrt{2}-3\sqrt{2}$

= $(6+20-3)\sqrt{2}$

= $23\sqrt{2}$

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