Respuesta :

Answer:

16.0857079

Step-by-step explanation:

first

you go to Google

second

yousearch up how do u solve the square root of 258.75

Answer:

The square root of 258.75 is [tex]\frac{3 \sqrt{115}}{2}[/tex]

Solution:

Here we have to find the square root of 258.75. First we convert the decimal value into a fraction value. Converting 258.75 in fraction we get

[tex]\frac{258.75 \times 100}{100}[/tex]

[tex]=\frac{25875}{100}[/tex]

Now we find the factors of 25875 and 100

Factors of 25875 = [tex]3 \times 3 \times 5 \times 5 \times 5 \times 23[/tex]

Since we have to find the square root, we group two same numbers together and place them outside square root. Grouping two threes and two five’s we get square root of  

[tex]25875=3 \times 5 \sqrt{5 \times 23}[/tex]

[tex]=15 \sqrt{115}[/tex]

Now the factors of 100 = [tex]2 \times 2 \times 5 \times 5[/tex]

The square root of 100 = [tex]2 \times 5[/tex] = 10

[tex]\text { Square root } \sqrt{258.75}=\frac{\sqrt{25875}}{\sqrt{100}}[/tex]

[tex]=\frac{15 \sqrt{115}}{10}[/tex]

Cancelling the numerator and denominator by 5, we get

[tex]=\frac{3 \sqrt{115}}{2}[/tex]

Hence the square root of 258.75 is [tex]\frac{3 \sqrt{115}}{2}[/tex]