Question

Simplify 1)  root 45 - 3 root 20 +4 Root 5

Answer 1

$\sqrt{45}-3 \sqrt{20} +4 \sqrt{5}$

= $\sqrt{9*5} - 3 \sqrt{4*5} +4 \sqrt{5}$

= $3\sqrt{5} - 6 \sqrt{5} +4 \sqrt{5}$

= $\sqrt{5}$

Answer 2

Answer:

The value of $\sqrt 45-3\sqrt 20+4\sqrt5$ after simplification is $\sqrt 5$

To find:

The value of $\sqrt 45-3\sqrt 20+4\sqrt5$ after simplifying its terms.

Solution:

Given that  

$\sqrt 45-3\sqrt 20+4\sqrt5$

To simplify the roots, split out the values in the roots.

$\begin{array} { l } { \sqrt { 45 } = \sqrt { 3 \times 3 \times 5 } } \\\\ { \sqrt { 20 } = \sqrt { 2 \times 2 \times 5 } } \end{array}$

$\sqrt 45-3\sqrt 20+4\sqrt5$

$\begin{array} { c } { = \sqrt { 3 \times 3 \times 5 } - 3 \sqrt { 2 \times 2 \times 5 } + 4 \sqrt { 5 } } \\\\ { = 3 \sqrt { 5 } - 3 \times 2 \sqrt { 5 } + 4 \sqrt { 5 } } \\\\ { = 3 \sqrt { 5 } - 6 \sqrt { 5 } + 4 \sqrt { 5 } } \\\\ { = 7 \sqrt { 5 } - 6 \sqrt { 5 } } \\\\ { = \sqrt { 5 } ( 1 - 6 ) } \\\\ { = \sqrt { 5 } ( 1 ) } \\\\ { = \sqrt { 5 } } \end{array}$

$\sqrt 45-3\sqrt 20+4\sqrt 5=\sqrt 5$

The value of $\sqrt 45-3\sqrt 20+4\sqrt5$ after simplification is $\sqrt5$