Which point on the number line shows the position of square root 78 a b c d
To determine the position of √78 on the number line, we must first find an approximation of its value. √78 is between √64 (which equals 8) and √81 (which equals 9) since 78 lies between 64 and 81. We can also calculate more precisely by using a calculator or estimating methods.
Using quick estimation, we can break down 78 into factors of 2 and 3:
78 = 2 × 3 × 13
Taking the square root, we have:
√78 = √(2 × 3 × 13)
Simplifying, we have:
√78 ≈ √(2) × √(3) × √(13)
√78 ≈ √(2) × √(3) × √(13)
√78 ≈ 1.41 × 1.73 × 3.61
Rounding to a reasonable approximation:
√78 ≈ 4.90
On the number line, √78 would be located between 4 and 5, closer to 5. So, the point on the number line that represents the position of √78 is closer to d.