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Aquí están las expresiones simplificadas:
1. \( \sqrt{60 b^{2} c} \times 2 b \sqrt{15} c = 60b^{2}\sqrt{c} \times c \)
2. \( \sqrt{\frac{600 x}{9 y^{2}}} \times \frac{10 \sqrt{6 y}}{3 y} = \frac{200\sqrt{xy}}{3y^{2}} \)
3. \( \sqrt{2400 k^{2} l^{2}} \div 10 k \sqrt{24} = l \)
4. \( \sqrt{\frac{7 m^{2}}{225 n^{2}}} \times \frac{m \sqrt{7}}{15 n} = \frac{7m^{2}}{225n^{2}} \)
5. \( \sqrt{120 h^{2}} = 2\sqrt{30} \times h \)
6. \( \sqrt{\frac{65 y}{16 z^{2}}} = \frac{\sqrt{65y}}{4z} \)
Solución
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 \( \sqrt{\frac{65 y}{16 z^{2}}} \):
\[
\frac{\sqrt{65y}}{4z}
\]
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