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Which is greater √6 + √3 or √7 + √2?
Type your answer as
1 for √6 + √3
2 for √7 + √2
Answer: 1
If a and b > 0 and a2 > b2, then a > b.
We have √6 + √3 and √7 + √2
Squaring both the terms
(6 + 3 + 2√18) and (7 + 2 + 2√14)
(9 + 2√18) and (9 + 2√14)
Since, rational part is same in both these terms, the term with greater irrational part will be greater,
∴ 9 + 2√18 > 9 + 2√14
⇒ √6 + √3 > √7 + √2
Hence, 1.
Which is greater √8 + √3 or √12 + √2?
Type your answer as
1 for √8 + √3
2 for √12 + √2
Answer: 2
If a and b > 0 and a2 > b2, then a > b.
We have √8 + √3 and √12 + √2
Squaring both the terms
(8 + 3 + 2√24) and (12 + 2 + 2√24)
(11 + 2√18) and (14 + 2√14)
Since, irrational part is same in both these terms, the term with greater rational part will be greater,
∴ 14 + 2√24 > 11 + 2√24
⇒ √12 + √2 > √8 + √3
Hence, 2.
Which is greater √5 - √2 or √4 - √3?
Type your answer as
1 for √5 - √2
2 for √4 - √3
Answer: 1
This is very straighforward question.
Here,
√5 > √4 and
√2 < √3
Hence, √5 - √2 > √4 - √3
In the first expression, a lower number √2 is bein subtracted from a higher number √5.
Hence, 1.
Which is greater √6 - √3 or √10 - √7?
Type your answer as
1 for √6 - √3
2 for √10 - √7
Answer: 1
Assuming √6 - √3 < √10 - √7
⇒ √6 + √7 < √10 + √3
Squaring both sides, we get
(13 + 2√42) < (13 + 2√30)
But this is not true.
∴ Our assumption was wrong.
⇒ √6 - √3 > √10 - √7.
Hence, 1.
Which is greater √13 + √11 or √15 + √10?
Type your answer as
1 for √13 + √11
2 for √15 + √10
Answer: 2
We have (√13 + √11) and (√15 + √10)
Squaring both sides we get
(24 + 2√143) and (25 + 2√150)
Since 25 > 24 and also 2√150 > 2√143
⇒ √15 + √10 > √13 + √11
Hence, 2.