root 45-3root20+4root5
Answers
The value of \sqrt 45-3\sqrt 20+4\sqrt5
4
5−3
2
0+4
5
after simplification is \sqrt 5
5
To find:
The value of \sqrt 45-3\sqrt 20+4\sqrt5
4
5−3
2
0+4
5
after simplifying its terms.
Solution:
Given that
\sqrt 45-3\sqrt 20+4\sqrt5
4
5−3
2
0+4
5
To simplify the roots, split out the values in the roots.
\begin{gathered}\begin{array} { l } { \sqrt { 45 } = \sqrt { 3 \times 3 \times 5 } } \\\\ { \sqrt { 20 } = \sqrt { 2 \times 2 \times 5 } } \end{array}\end{gathered}
45
=
3×3×5
20
=
2×2×5
\sqrt 45-3\sqrt 20+4\sqrt5
4
5−3
2
0+4
5
\begin{gathered}\begin{array} { c } { = \sqrt { 3 \times 3 \times 5 } - 3 \sqrt { 2 \times 2 \times 5 } + 4 \sqrt { 5 } } \\\\ { = 3 \sqrt { 5 } - 3 \times 2 \sqrt { 5 } + 4 \sqrt { 5 } } \\\\ { = 3 \sqrt { 5 } - 6 \sqrt { 5 } + 4 \sqrt { 5 } } \\\\ { = 7 \sqrt { 5 } - 6 \sqrt { 5 } } \\\\ { = \sqrt { 5 } ( 1 - 6 ) } \\\\ { = \sqrt { 5 } ( 1 ) } \\\\ { = \sqrt { 5 } } \end{array}\end{gathered}
=
3×3×5
−3
2×2×5
+4
5
=3
5
−3×2
5
+4
5
=3
5
−6
5
+4
5
=7
5
−6
5
=
5
(1−6)
=
5
(1)
=
5
\sqrt 45-3\sqrt 20+4\sqrt 5=\sqrt 5
4
5−3
2
0+4
5
=
5
The value of \sqrt 45-3\sqrt 20+4\sqrt5
4
5−3
2
0+4
5
after simplification is \sqrt5
5
root 45-3root20+4root5
45-3 = 42
20+4=24
42+24=66
so we have to divide to find root
66÷5=13.2
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