Let's reduce: ${(7\times \sqrt{5})}^2$

ⓘ The power of a product is the product of the powers: ${(7\times \sqrt{5})}^2$ = $7^2\times {\left(\sqrt{5}\right)}^2$

$7^2\times {\left(\sqrt{5}\right)}^2$

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product: $7^2$ = $7\times 7$ = $49$■A power of a power multiplies the exponents, (a^n)^m = a^(n*m): ${\left(\sqrt{5}\right)}^2$ = $5^{\frac{1}{2}\times 2}$

$49\times 5^{\frac{1}{2}\times 2}$

ⓘ Multiplying a fraction by a number multiplies its numerator: $\frac{1}{2}\times 2$ = $\frac{1\times 2}{2}$ = $\frac{2}{2}$■We simplify the fraction by dividing the numerator and the denominator by $2$, their greatest common divisor: $\frac{2}{2}$ = $1$

$49\times 5^1$

ⅰ $49\times 5$ = $(40+9)\times 5$ = $40\times 5+9\times 5$ = $200+45$ = $245$

▶Simplified form:   $245$