Question

Simplify the radical expression.

Answer 1

Answer:

1) D. $6\sqrt{120}$, 2) C. $2\sqrt{56}q^{2}$, 3) C. $\frac{4\sqrt{11}}{11}$

Step-by-step explanation:

1) We proceed to simplify the expression given in statement:

(i) $2\sqrt{10}\cdot 3\sqrt{12}$ Given

(ii) $(3\cdot 2)\cdot (\sqrt{10}\cdot \sqrt{12})$ Commutative and associative properties

(iii) $(3\cdot 2)\cdot (10^{0.5}\cdot 12^{0.5})$ Definition of square root.

(iv) $6\cdot (10\cdot 12)^{0.5}$ Definition of multiplication/$a^{c}\cdot b^{c} = (a\cdot b)^{c}$

(v) $6\sqrt{120}$ Definition of multiplication/Definition of square root/Result

Answer: D

2) We proceed to simplify the expression given in statement:

(i) $\sqrt{14}q \cdot 2\sqrt{4}q$ Given

(ii) $2\cdot (\sqrt{14}\cdot \sqrt{4})\cdot (q\cdot q)$ Commutative and associative properties

(iii) $2\cdot (14^{0.5}\cdot 4^{0.5})\cdot q^{2}$ Definition of square root/Definition of power.

(iv) $2\cdot (14\cdot 4)^{0.5}\cdot q^{2}$    $a^{c}\cdot b^{c} = (a\cdot b)^{c}$

(v) $2\sqrt{56}q^{2}$ Definition of multiplication/Definition of square root/Result

Answer: C

3) We proceed to simplify the expression given in statement:

(i) $\frac{4}{\sqrt{11}}$ Given

(ii) $\frac{4}{\sqrt{11}}\cdot \frac{\sqrt{11}}{\sqrt{11}}$ Modulative property/Existence of multiplicative inverse.

(iii) $\frac{4\sqrt{11}}{\sqrt{11}\cdot \sqrt{11}}$  $\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot c}{b\cdot d}$

(iv) $\frac{4\sqrt{11}}{11^{0.5}\cdot 11^{0.5}}$ Definition of square root.

(v) $\frac{4\sqrt{11}}{11}$ $a^m\cdot a^{n} = a^{m+n}$/Result

Answer: C