Question

Find next one 2√3,2√5,√30,√42,2√14 ?

Answer 1

Answer:

i think √ 16 is the next one

Answer 2

Answer:

Given series : $2\sqrt{3} ,2\sqrt{5} ,\sqrt{30},\sqrt{42},2\sqrt{14}, ?$.

Answer: $2\sqrt{3} ,2\sqrt{5} ,\sqrt{30},\sqrt{42},2\sqrt{14}, 6\sqrt{2}$

Step-by-step explanation:

• For the given question we should find the combination between each terms in the series.
• That is, first term: $2\sqrt{3}= \sqrt{2*2*3}=\sqrt{3*4}$

                    2nd term: $2\sqrt{5}= \sqrt{2*2*5}=\sqrt{4*5}$

                    3rd term : $\sqrt{30}= \sqrt{2*3*5}=\sqrt{5*6}$

                    4th term : $\sqrt{42}= \sqrt{2*3*7}=\sqrt{6*7}$

                    5th term : $2\sqrt{14}= \sqrt{2*2*2*7}=\sqrt{7*8}$

• Similarly, 6th term should be the multiplication of square root of 7 and 8.
• That is, 6th term: $\sqrt{8*9}=\sqrt{2*2*2*3*3}$.

                      $\sqrt{2*2*2*3*3}=(2*3)\sqrt{2}$  => ($\sqrt{2*2}=2$ square root rule)

                                      $\sqrt{8*9}=6\sqrt{2}$

• Final Answer: next number is:  $6\sqrt{2}$