Simplify the expression. 14. \( \sqrt{60 b^{2} c} 2 b \sqrt{15} c \) 17. \( \sqrt{\frac{600 x}{9 y^{2}}} \frac{10 \sqrt{6 y}}{3 y} \) 15. \( \sqrt{2400 k^{2} l^{2}}, 10 k \backslash \sqrt{24} \) 18. \( \sqrt{\frac{7 m^{2}}{225 n^{2}}} \frac{m \sqrt{7}}{15 n} \) 16. \( \sqrt{120 h^{2}} \) 19. \( \sqrt{\frac{65 y}{16 z^{2}}} \)

Simplify the expression by following steps: - step0: Solution: \(\sqrt{\frac{65y}{16z^{2}}}\) - step1: Use the properties of radicals: \(\frac{\sqrt{65y}}{\sqrt{16z^{2}}}\) - step2: Simplify the expression: \(\frac{\sqrt{65y}}{4z}\) Calculate or simplify the expression \( \sqrt(2400*k^2*l^2)/(10*k*\sqrt(24)) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\sqrt{2400k^{2}l^{2}}}{\left(10k\sqrt{24}\right)}\) - step1: Remove the parentheses: \(\frac{\sqrt{2400k^{2}l^{2}}}{10k\sqrt{24}}\) - step2: Simplify the root: \(\frac{\sqrt{2400k^{2}l^{2}}}{10k\times 2\sqrt{6}}\) - step3: Simplify the root: \(\frac{20\sqrt{6}\times lk}{10k\times 2\sqrt{6}}\) - step4: Multiply the terms: \(\frac{20\sqrt{6}\times lk}{20k\sqrt{6}}\) - step5: Reduce the fraction: \(l\) Calculate or simplify the expression \( \sqrt(60*b^2*c)*2*b*\sqrt(15)*c \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{60b^{2}c}\times 2b\sqrt{15}\times c\) - step1: Simplify the root: \(2b\sqrt{15c}\times 2b\sqrt{15}\times c\) - step2: Multiply the terms: \(4b\sqrt{15c}\times b\sqrt{15}\times c\) - step3: Multiply the terms: \(4b^{2}\sqrt{15c}\times \sqrt{15}\times c\) - step4: Multiply: \(60b^{2}\sqrt{c}\times c\) Calculate or simplify the expression \( \sqrt((7*m^2)/(225*n^2))*(m*\sqrt(7))/(15*n) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\sqrt{\frac{7m^{2}}{225n^{2}}}\times \left(m\sqrt{7}\right)}{15n}\) - step1: Remove the parentheses: \(\frac{\sqrt{\frac{7m^{2}}{225n^{2}}}\times m\sqrt{7}}{15n}\) - step2: Simplify the root: \(\frac{\frac{\sqrt{7}\times m}{15n}\times m\sqrt{7}}{15n}\) - step3: Multiply the terms: \(\frac{\frac{7m^{2}}{15n}}{15n}\) - step4: Multiply by the reciprocal: \(\frac{7m^{2}}{15n}\times \frac{1}{15n}\) - step5: Multiply the terms: \(\frac{7m^{2}}{15n\times 15n}\) - step6: Multiply the terms: \(\frac{7m^{2}}{225n^{2}}\) Calculate or simplify the expression \( \sqrt(120*h^2) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{120h^{2}}\) - step1: Write as a product: \(\sqrt{4\times 30h^{2}}\) - step2: Write in exponential form: \(\sqrt{2^{2}\times 30h^{2}}\) - step3: Reorder the terms: \(\sqrt{2^{2}h^{2}\times 30}\) - step4: Use the properties of radicals: \(\sqrt{2^{2}h^{2}}\times \sqrt{30}\) - step5: Simplify the root: \(2\sqrt{30}\times h\) Calculate or simplify the expression \( \sqrt(600*x/(9*y^2))*10*\sqrt(6*y)/(3*y) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\sqrt{\frac{600x}{9y^{2}}}\times 10\sqrt{6y}}{3y}\) - step1: Reduce the fraction: \(\frac{\sqrt{\frac{200x}{3y^{2}}}\times 10\sqrt{6y}}{3y}\) - step2: Simplify the root: \(\frac{\frac{10\sqrt{2x}}{\sqrt{3}\times y}\times 10\sqrt{6y}}{3y}\) - step3: Multiply the terms: \(\frac{\frac{200\sqrt{3yx}}{\sqrt{3}\times y}}{3y}\) - step4: Multiply by the reciprocal: \(\frac{200\sqrt{3yx}}{\sqrt{3}\times y}\times \frac{1}{3y}\) - step5: Multiply the terms: \(\frac{200\sqrt{3yx}}{\sqrt{3}\times y\times 3y}\) - step6: Multiply the terms: \(\frac{200\sqrt{3yx}}{3\sqrt{3}\times y^{2}}\) - step7: Simplify: \(\frac{200\sqrt{xy}}{3y^{2}}\) Aquí están las expresiones simplificadas: 1. Para \( \sqrt{60 b^{2} c} 2 b \sqrt{15} c \): \[ 60b^{2}\sqrt{c}\times c \] 2. Para \( \sqrt{\frac{600 x}{9 y^{2}}} \frac{10 \sqrt{6 y}}{3 y} \): \[ \frac{200\sqrt{xy}}{3y^{2}} \] 3. Para \( \sqrt{2400 k^{2} l^{2}} \div 10 k \sqrt{24} \): \[ l \] 4. Para \( \sqrt{\frac{7 m^{2}}{225 n^{2}}} \frac{m \sqrt{7}}{15 n} \): \[ \frac{7m^{2}}{225n^{2}} \] 5. Para \( \sqrt{120 h^{2}} \): \[ 2\sqrt{30}\times h \] 6. Para \( \sqrt{\frac{65 y}{16 z^{2}}} \): \[ \frac{\sqrt{65y}}{4z} \]