Complete question is;
Which of the following can be reduced to a single number in standard form?
A) 3√3 + 5√8
B) 2√5 + 5√45
C) √7 + √9
D) 4√2 + 3√6
Answer:
Only option B) 2√5 + 5√45 can be reduced to a single number
Explanation:
A) For 3√3 + 5√8;
Let's simplify it to get;
3√3 + 5√(4 × 2)
From this, we get;
3√3 + (5 × 2)√2 = 3√3 + 10√2
This is 2 numbers and not a single number. Thus it can't be reduced to a single number in standard form.
B) 2√5 + 5√45
Simplifying to get;
2√5 + 5√(9 × 5)
This gives;
2√5 + (5 × 3)√5 = 2√5 + 15√5
Adding the surds gives;
17√5.
This is a single number and thus can be reduced to a single number
C) For √7 + √9
Simplifying, to get;
√7 + 3.
This is 2 numbers and not a single number. Thus it can't be reduced to a single number in standard form.
D) 4√2 + 3√6
Thus can't be simplified further because both numbers inside the square root don't have factors that are perfect squares.
Thus, it remains 2 numbers and not a single number and can't be reduced to a single number in standard form.
