The first ten days of Dhul-Hijjah are venerated days. Allah swore by them in His Book, and swearing by a thing is indicative of its importance and great benefit. Allah says (interpretation of the meaning):

“By the dawn; By the ten nights (i.e. the first ten days of the month of Dhul-Hijjah)” [Al-Fajr 89:1]

Ibn ‘Abbas, Ibn al-Zubayr, Mujahid and others among the earlier and later generations said: This refers to the ten days of Dhu’l-Hijjah. Ibn Kathir said: This is the correct view. (Tafsir Ibn Kathir, 8/413)

 Good deeds during these days are beloved to Allah, because the Prophet (peace and blessings of Allah be upon him) said: “There are no days in which righteous deeds are more beloved to Allah than these ten days.” They said, “O Messenger of Allah, not even jihad for the sake of Allah?” The Messenger of Allah (peace and blessings of Allah be upon him) said, “Not even jihad for the sake of Allah, except in the case of a man who went out to fight, giving himself and his wealth up for the cause, and came back with nothing.” Narrated by al-Bukhari, 969; al-Tirmidhi, 757. This version was narrated by al-Tirmidhi and classed as sahih by al-Albani in Sahih al-Tirmidhi, 605. 

One of the righteous deeds during these days is to remember Allah by reciting takbir (saying “Allahu akbar”) and tahlil (saying “La ilaha ill-Allah”), because of the following evidence. 

Allah says (interpretation of the meaning): 

“That they may witness things that are of benefit to them (i.e. reward of Hajj in the Hereafter, and also some worldly gain from trade), and mention the Name of Allah on appointed days” [Al-Hajj 22:28]

The “appointed days” are the first ten days of Dhu’l-Hijjah. 

Allah says (interpretation of the meaning): 

“And remember Allah during the appointed Days” [Al-Baqarah 2:203]

These are the days of al-Tashriq, i.e. the 11th, 12th and 13th of Dhul-Hijjah. 

The Prophet (peace and blessings of Allah be upon him) said: “The days of tashriq are the days of eating, drinking and remembering Allah.” (Narrated by Muslim, 1141)