simplify
√72 + √800 - √81
Answers
Answer:
Answer:
\sqrt{72}+\sqrt{800}-\sqrt{18}
72
+
800
−
18
=23\sqrt{2}23
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}
72
</p><p>=
2
2
×3
2
×2
= 2\times 3 \sqrt{2}2×3
2
= 6\sqrt{2}6
2
----(1)
b) \sqrt{800} = \sqrt{2^{4}\times 2 \times 5^{2}}
800
=
2
4
×2×5
2
= 2^{2}\times 5 \sqrt{2}2
2
×5
2
= 20\sqrt{2}20
2
-----(2)
c)\sqrt{18} = \sqrt{2 \times 3^{2}}
18
=
2×3
2
=3\sqrt{2}3
2
---(3)
Therefore,
\sqrt{72}+\sqrt{800}-\sqrt{18}
72
+
800
−
18
=6\sqrt{2}+20\sqrt{2}-3\sqrt{2}6
2
+20
2
−3
2
= (6+20-3)\sqrt{2}(6+20−3)
2
= 23\sqrt{2}23
2
•••
Answer:
Step-by-step explanation:
