Question

$$\sqrt{ { \left(-4-1 \right) }^{ 2 } + { \left(4-7 \right) }^{ 2 } }$$

Answer

sqrt(34)

Solution


Simplify  \(-4-1\)  to  \(-5\).
\[\sqrt{{(-5)}^{2}+{(4-7)}^{2}}\]
Simplify  \(4-7\)  to  \(-3\).
\[\sqrt{{(-5)}^{2}+{(-3)}^{2}}\]
Since the power of 2 is even, the result will be positive.
\[\sqrt{{5}^{2}+{(-3)}^{2}}\]
Simplify  \({5}^{2}\)  to  \(25\).
\[\sqrt{25+{(-3)}^{2}}\]
Since the power of 2 is even, the result will be positive.
\[\sqrt{25+{3}^{2}}\]
Simplify  \({3}^{2}\)  to  \(9\).
\[\sqrt{25+9}\]
Simplify  \(25+9\)  to  \(34\).
\[\sqrt{34}\]

Decimal Form: 5.830952