If n is a positive whole number write (n square root 15 – square root 5)^2 in the form a+b square root 3

Here is your answer,

Q. If the √2 = 1.414 , √5 = 2.236 and √3 = 1.732 ,find the value of -

\begin{gathered}(1) \: \: \sqrt{72} + \sqrt{48} \\ \\ \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ \\ 6 \sqrt{2} + 4 \sqrt{3} \\ \\ 6 \times 1.414 + 4 \times 1.732 \\ \\ 8.484 + 6.928 \\ \\ 15.412\end{gathered}

(1)

72

+

48

2×2×2×3×3

+

2×2×2×2×3

6

2

+4

3

6×1.414+4×1.732

8.484+6.928

15.412

\begin{gathered}(2) \: \: \sqrt{ \frac{125}{64} } \\ \\ \frac{ \sqrt{125} }{ \sqrt{64} } \\ \\ \frac{ \sqrt{5 \times 5 \times 5} }{ \sqrt{8 \times 8} } \\ \\ \frac{5 \sqrt{5} }{8} \\ \\ \frac{5 \times 2.236}{8} \\ \\ \frac{11.180}{8} \\ \\ 1.3975\end{gathered}

(2)

64

125

64

125

8×8

5×5×5

8

5

5

8

5×2.236

8

11.180

1.3975

Hence,

\begin{gathered}(1) \: \: \sqrt{72} + \sqrt{48} = 15.412 \\ \\ (2) \: \: \sqrt{ \frac{125}{64} } = 1.3975\end{gathered}

(1)

72

+

48

=15.412

(2)

64

125

=1.3975

Hope it helps.

no problobm

step-by-step explanation: