Which one of the following is true?
Last updated Jun 19, 2026
Correct Answer:
Option A —
sqrt(5) + sqrt(3) >sqrt(6) + sqrt(2)
To find out which statement is true, we can compare the two main expressions by squaring them. Squaring positive numbers lets us compare their sizes easily without changing which one is bigger.Squaring the first expression (the square root of five plus the square root of three):
When you square this combination, you add the two numbers inside the roots (five plus three, which equals eight).
Then, you add two times the square root of their product (five times three, which is fifteen).
This gives a total of: eight plus two times the square root of fifteen.
Squaring the second expression (the square root of six plus the square root of two):
When you square this combination, you also add the two numbers inside the roots (six plus two, which equals eight).
Then, you add two times the square root of their product (six times two, which is twelve).
This gives a total of: eight plus two times the square root of twelve.
Comparing the two results:
Both results start with the number eight.
Now we just compare the remaining parts: two times the square root of fifteen versus two times the square root of twelve.
Since fifteen is larger than twelve, the square root of fifteen is larger than the square root of twelve.
Therefore, the first result is larger than the second result.
Because the squared version of the first expression is larger, the original expression itself must also be larger. This means the square root of five plus the square root of three is greater than the square root of six plus the square root of two.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
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