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Answer:
14 + 6√5
= 9+ 5 + 6√5 ( splitting 14 as 9+5)
= 3^2 + √5^2+ 6√5
= 3^2 + 6√5 + √5^2
= 3^2+ 2*3*√5+ √5^2
= a^2 + 2ab+ b^2 = (a+b)^2
Hence
14+6√5 = ( 3+ √5)^2
Square root of 14 + 6√5 = square root of (3+√5)^2
Square root of 14 + 6√ 5 = 3 + √5
Ans : 3+√5
Step-by-step explanation:
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Tip: Always write the irrational term in form of 2 × a × b. For example, 12√5 = 2(6)(√5). Now you know what is a and b. So, compare it w/ the identities and find the match.
Answer: 3 + √5.
Explanation:
√(14 + 6√5)
= √[14 + 2(3)(√5)]
= √[(3)^2 + (√5)^2 + 2(3)(√5)]
= √(3 + √5)^2
= (3 + √5).