Simplify the following surd.Square root of 16/9.square root of 8+square root 18 +square root 50.Plz explain in detail
√(16/9) = √16 / √9 = 4/3
√8 + √18 + √50 = √(4*2) + √(9*2) + √(25*2) = 2√2 + 3√2 + 5√2 = 10√2
Thanku so much
To simplify the given surds, we need to simplify the individual surds first and then combine them.
1. Simplifying √(16/9):
First, we simplify the numerator and denominator separately. The square root of 16 is 4, and the square root of 9 is 3. Therefore, we get √(16/9) = 4/3.
2. Simplifying √8, √18, and √50:
We need to find the factors of each number under the square root to simplify them.
a) √8:
The factors of 8 are 1, 2, 4, and 8. Since 2 is the largest perfect square factor, we can express √8 as √(4 * 2). The square root of 4 is 2, so we get √8 = 2√2.
b) √18:
The factors of 18 are 1, 2, 3, 6, 9, and 18. Since 9 is the largest perfect square factor, we can express √18 as √(9 * 2). The square root of 9 is 3, so we get √18 = 3√2.
c) √50:
The factors of 50 are 1, 2, 5, 10, 25, and 50. Since 25 is the largest perfect square factor, we can express √50 as √(25 * 2). The square root of 25 is 5, so we get √50 = 5√2.
3. Combining the simplified surds:
Now, we can combine the simplified surds by adding them together. Thus, the simplified surd becomes:
√(16/9) + √8 + √18 + √50
= 4/3 + 2√2 + 3√2 + 5√2
Since all terms involve the square root of 2, we can combine them:
= 4/3 + (2 + 3 + 5)√2
= 4/3 + 10√2
Therefore, the simplified surd is 4/3 + 10√2.